a first embodiment of the present invention is an improvement to the drive method used by the liquid crystal display device of fig1 and its internal configuration and functions are those of the device of fig1 that has already been described . note that the non - linear elements 114 of fig1 and fig1 that are used in the method of driving a liquid crystal display device in accordance with the present invention , as described as embodiments 1 to 6 herein , could be mim elements , mis elements , varistors , ring diodes , or back - to - back diodes . note also that an mim element could be configured with one metal layer thereof being a transparent conductive layer which can be made to serve also as a transparent electrode of the liquid - crystal panel . further , the insulator layer of the mim element could be a silicon nitride . in these embodiments , scanning signals are supplied to row electrodes , and data signals are supplied to column electrodes as shown in fig1 . alternatively , it is also possible to supply scanning signals to column electrodes , and to supply data signals to row electrodes . the timing chart of the first embodiment is illustrated in fig1 and fig1 . fig1 is a timing chart of the y driver which is necessary for carrying out the first embodiment of the present invention . note that the dy , yscl , fry , c 1 , and cn signals are the same as those that have already been described with reference to fig5 . y driver outputs the selection voltage signal vs as the output vn when the selection signal cn is 1 in the same way , but in order to carry out this first embodiment , the phase relationship between the selection signal cn and the ac inversion signal fry is changed . in the prior art drive ( see fig5 ), the timing at which cn and fry switch is the same , but in this first embodiment their phase relationship is shifted so that the phase of fry is changed in the time period when cn = 1 . fig1 illustrates this change in detail . the left - hand side of fig1 shows that when cn is 1 and the selection voltage signal vs is being output as the output vn , fry switches from 1 to 0 . since the potential of the selection voltage signal vs switches by switching of fry ( when fry = 1 , vs = vp ; when fry = 0 , vs =− vp ), the potential − vp changes into vp after switching of fry . similarly , the right - hand side of fig1 shows the opposite case for yn when cn = 1 , where fry switches from 0 to 1 . in this case , the potential vp changes into − vp after the switch in fry . in this embodiment , the switch in fry is set to occur in the ending part of the period during which cn = 1 , so the duty ratio is increased in this ending part , but this change in the phase relationship between cn and fry enables this duty ratio to be freely selected . the actual drive created by combining the operation of the above - described y driver and the x driver will now be described with reference to fig1 . this figure shows the waveforms of signals applied to the pixel that is the mth pixel in the horizontal direction and the nth pixel in the vertical direction , in the liquid crystal panel 115 of fig1 in the same manner as already described for fig6 . the column electrode signal xm sequentially samples the ac video signal 104 , holds the data for one horizontal scanning period , then outputs the data , in the same way as in the prior art , so that the output data itself represents the data for the previous horizontal scanning period . the row electrode signal yn is the same as the signal in fig1 , which was described above . in this case , one horizontal scanning period is the period obtained by multiplying one field period by the number of data lines ( the number of column electrodes ). if a rest period is set for a certain column electrode , only column electrodes that do not have a rest period set for them are included in the calculation . now look at the difference signal xm − yn between the column electrode signal xm and the row electrode signal yn , both of which are actually applied to the non - linear element 114 and liquid crystal layer 113 . the column electrode signal xm outputs the same level within one horizontal scanning period , but the polarity of the row electrode signal yn inverts greatly during one horizontal scanning period . therefore , the polarity of the difference signal also changes greatly between positive and negative , as shown at the bottom of fig1 . on the left - hand side of fig1 , large potential of positive polarity is applied to the pixel , then the potential swings over greatly to the negative polarity side . on the right - hand side of fig1 , after application of large negative potential to the pixel , the potential changes greatly to positive polarity . it can be seen from fig1 that the pixel is selected twice , i . e ., in two selection periods , ta and tb , within one horizontal scanning period . when the non - linear element 114 is selected twice , the second selection determines the gradation value . therefore , as shown in fig1 , it is the selection of the ending period tb that determines the display gradation ( in the example on the right - hand side of the figure , this is a write at positive polarity side ). this means that , with the drive of fig1 , a display gradation ( or rather , the root - mean - square value actually applied to the liquid crystal layer 113 ) has the same effect as that of fig6 . a point that should be noted is the potential of the difference signal xm − yn in each of the initial period ta and the ending period tb of one horizontal scanning period . as described above , the display gradation is determined by the ending selection . regarding the initial selection , the selection data for the initial period ta is the complement of the data of the ending period tb in this first embodiment . note that in this case , “ complement ” is defined here as either of two numbers which together achieve a level of 100 %. for example , 0 is the complement of 1 , and 0 . 9 is the complement of 0 . 1 . the state of the column electrode signal described below shows the reason for this complementary relationship . in the following description , the pixels show a white display when a voltage equal to or more than the threshold voltage is applied to the liquid crystal layer and show a black display when a voltage less than the threshold voltage is applied to the liquid crystal layer . this mode of display is defined here as a negative display . in the case of applying a voltage of positive polarity to the liquid crystal layer , the potential of the column electrode signal is va when the pixels show a white display and − va when the pixels show a black display . conversely , in the case of applying a voltage of negaive polarity to the liquid crystal layer , the potential of the column electrode signal is − va when the pixels show a white display and va when the pixels show a black display . when the data to be displayed is white and a voltage to be applied is positive polarity , the potential of the column electrode signal is va . when the data to be displayed is black and a voltage to be applied is negative polarity , the potential of the column electrode signal is also va . in other words , the complement relationship defined above for the column electrode signal is valid when viewed from the viewpoint of positive and negative polarity . it should be clear from fig1 that an intermediate display would function in exactly the same manner . in such a case , with the drive of fig1 , to correspond with the selection that will determine the display gradation in the ending period tb ( hereinafter referred to as the “ actual selection ”), data that is the complement thereof is written in the initial period ta ( hereinafter referred to as the “ compensatory selection ”). this operation enables a reduction in afterimages caused by i - v characteristic shift in the non - linear elements . the principle by which the first embodiment can reduce the afterimages in the non - linear elements caused by i - v characteristic shift will now be described in detail with reference to fig1 . the description first concerns a white display , shown in the left - hand side of fig1 . in order to display white , the write potential for the actual selection in the ending period tb is at a maximum at | vp + va |. the compensatory selection in the initial period ta writes data that is the complement thereof , and so is at the minimum potential of | vp − va |. conversely , when black is displayed ( corresponding to the right - hand side of fig1 ), the write potential for the actual selection in the ending period tb is at a minimum at | vp − va |, and the compensatory selection in the initial period ta is at a maximum of | vp + va |. when white is selected , a large potential is applied to the non - linear element during the actual selection , but only a small potential is applied to the non - linear element in the preceding compensatory selection . conversely , when black is selected , the potential to be applied in the actual selection is small , but a large potential is applied to the non - linear element during the compensatory selection . this means that the total potential applied to the non - linear element can be made the same , regardless of whether black or white is selected . to be precise , if the effective voltage vmw for white display and the effective voltage vmb for black display which are applied to the non - linear element are made the same , the i - v characteristic shift of the non - linear element can be made uniform , and the phenomenon of afterimages caused by i - v characteristic shift can be eliminated . writing the conditions of fig1 as an equation gives : therefore , it is best to ensure that the values in the initial period ta ( the compensatory selection ) and the ending period tb ( the actual selection ) satisfy the above equation . in general , in the beginning of the compensatory selection period , the potential applied to the non - linear element changes to the compensatory selection potential from that applied in the non - selection period . on the left - hand side of fig1 , this potential goes from − 2va to −( vp − va ); on the right - hand side , it goes from 0 to −( vp + va ). in the beginning of the actual selection , however , the potential applied to the non - linear element changes much more , from the compensatory selection potential to the actual selection potential . on the left - hand side of fig1 , this potential goes from −( vp − va ) to ( vp + va ); on the right - hand side , it goes from −( vp + va ) to ( vp − va ). therefore , a larger potential is applied to the non - linear element for the actual selection , and consequently ta & gt ; tb . the enabling of a dramatic reduction in afterimages due to i - v characteristic shift of the non - linear element will now be described with reference to the example of fig1 . in the same way as described with reference to fig1 , the signal applied to pixel p 1 ( in other words , xm 1 − yn ) and the signal applied to pixel p 2 ( in other words , xm 2 − yn ) are shown in fig1 . pixel p 1 shows a black display and pixel p 2 shows a white display . when the display is switched to an intermediate display at this point , the principle described above dictates that the effective voltage vmsb applied to pixel p 1 and the effective voltage vmsw applied to pixel p 2 are equal , so the magnitude of i - v characteristic shift in the non - linear elements thereof is similarly equal . therefore , the effective voltage s 1 applied to pixel p 1 and the effective voltage s 2 applied to pixel p 2 during intermediate display are also equal , and thus the difference in brightness described with reference to fig1 can be eliminated . note that , for the purpose of facilitating understanding of this embodiment of the present invention , only the cases of black and white display were described , but the present invention is also capable of equalizing the i - v characteristic shift of non - linear elements under all display conditions . this means that the phenomenon of afterimages can be reduced , irrespective of the type of display . fig1 is a timing chart of the y driver which is necessary for carrying out a second embodiment of the present invention . note that the dy , yscl , fry , c 1 , and cn signals are the same as those that have already been described with reference to fig5 . the duty ratio of yscl is 50 % and it is used as a switching signal to switch the potential of the signal vs from ± vr to ± vp . in other words , vs is output in accordance with the following relationships : y driver outputs the selection voltage signal vs as the output vn when the selection signal cn is 1 but , in order to carry out this second embodiment , the phase relationship between the selection signal cn and the ac inversion signal fry is changed to make sure that | vr |& gt ;| vp |. in the prior art drive , the timing at which cn and fry switch is the same , but in this second embodiment , their phase relationship is shifted so that the phase of fry is changed in the time period when cn = 1 . fig1 illustrates this change in detail . the left - hand side of fig1 shows the selection voltage signal vs output as yn when cn is 1 . at this point , the above relationships dictate that vs is − vr and ouptputs relatively larger voltage than − vp . next , in the period in which cn = 1 , fry switches from 1 to 0 . at the same timing , yscl ( the vr and vp switching signal ) switches from 0 to 1 , so that vp is output as the selection voltage signal vs for yn . in other words , after the yn output is − vr , the switch in fry changes it to vp . the right - hand side of fig1 shows the opposite case for yn when cn = 1 ; where fry switches from 0 to 1 and yscl also switches from 0 to 1 . in this case , yn outputs − vp by switching in fry after yn outputs vr . in this embodiment , the switch in fry is set to occur in the middle of the period when cn = 1 , in such a manner that this period is divided evenly , but this duty ratio can be freely selected . the actual drive created by combining the operation of the above - described y driver and the x driver will now be described with reference to fig1 . fig1 shows the waveforms of signals applied to the pixel that is the mth pixel in the horizontal direction and the nth pixel in the vertical direction , in the liquid crystal panel 115 of fig1 in the same manner as already described for fig6 . the column electrode signal xm sequentially samples the ac video signal 104 , holds the data for one horizontal scanning period , then outputs the data , in the same way as in the prior art , so that the output data itself represents the data for the previous horizontal scanning period . the row electrode signal yn is the same as the signal in fig1 , which was described above . now look at the difference signal xm − yn between the column electrode signal xm and the row electrode signal yn , both of which are actually applied to the non - linear element 114 and liquid crystal layer 113 . the column electrode signal xm outputs the same level within one horizontal scanning period but the polarity of the row electrode signal yn inverts greatly during one horizontal scanning period . therefore , the polarity of the difference signal also changes greatly between positive and negative , as shown at the bottom of fig1 . therefore , in the same manner as in the first embodiment , there are two selection periods , ta and tb , within one horizontal scanning period . when the non - linear element 114 is selected twice , the second selection determine the gradation value . therefore , as shown in fig1 , it is the selection of the ending period tb that determines the display gradation ( in the example on the right - hand side of the figure , this is a write at positive polarity side ). this means that , with the drive of fig1 , a display gradation ( or rather , the root - mean - square value actually applied to the liquid crystal layer 113 ) has the same effect as that of fig6 . the selection data for the initial period ta is the complement of the data of the ending period tb , in the same manner as in the first embodiment . the reason for this is the same as that given for the first embodiment . therefore , with the drive of fig1 , corresponding to the actual selection for determining the display gradation in the ending period tb , the complementary data of the actual selection is written in the compensatory selection in the initial period ta . this operation enables a reduction in afterimages caused by i - v characteristic shift in the non - linear elements . the principle by which the second embodiment can reduce the afterimages in the non - linear elements caused by i - v characteristic shift will now be described in detail with reference to fig2 . the description first concerns a white display , shown in the left - hand side of fig2 . in order to show a white display by the pixels , the write potential for the actual selection in the ending period tb is at a maximum at | vp + va |. the compensatory selection in the initial period ta writes data that is the complement thereof , and so is at a minimum potential within the compensatory voltage | vr − va |. conversely , when the pixels show a black display ( corresponding to the right - hand side of fig2 ), the write potential for the actual selection in the ending period tb is at a minimum at | vp − va |, and the compensatory selection in the initial period ta is at a maximum of | vp + va |. when white is selected , a large potential is applied to the non - linear element during the actual selection , but only a small potential is applied to the non - linear element in the preceding compensatory selection . conversely , when black is selected , the potential to be applied for the actual selection is small , but a large potential is applied to the non - linear element during the compensatory selection . in other words , this means that the total potential applied to the non - linear element can be made the same , regardless of whether black or white is selected . to be precise , if the effective voltage vmw for white display and the effective voltage vmb for black display that are applied to the non - linear element are made the same , the i - v characteristic shift of the non - linear element can be made uniform , and the phenomenon of afterimages caused by i - v characteristic shift can be eliminated . writing the conditions of fig2 as an equation gives equation 3 . therefore , it is best to determine a selection voltage | vr | for the compensatory selection that satisfies equation 3 . in general , in the beginning of the compensatory selection period , the potential applied to the non - linear element changes to the compensatory selection potential from that applied in the non - selection period . on the left - hand side of fig2 , this potential goes from − 2va to −( vr − va ); on the right - hand side , it goes from 0 to −( vr + va ). in the beginning of the actual selection , however , the potential applied to the non - linear element changes much more , from the compensatory selection potential to the actual selection potential . on the left - hand side of fig2 , this potential goes from −( vp − va ) to ( vp + va ); on the right - hand side , it goes from −( vr + va ) to ( vp − va ). therefore , a larger potential is applied to the non - linear element for the actual selection , and consequently vr & gt ; vp . the enabling of a dramatic decrease in afterimages due to i - v characteristic shift of the non - linear element will now be described with reference to the example of fig2 . in the same way as described with reference to fig1 , the signal applied to pixel p 1 ( in other words , xm 1 − yn ) and the signal applied to pixel p 2 ( in other words , xm 2 − yn ) are shown in fig2 . pixel p 1 shows a black display and pixel p 2 shows a white display . when the display is switched to an intermediate display at this point , the principle described above dictates that the effective voltage vmsb applied to pixel p 1 and the effective voltage vmsw applied to pixel p 2 are equal , so the magnitude of i - v characteristic shift in these non - linear elements is similarly equal . therefore , the effective voltage s 1 applied to pixel p 1 and the effective voltage s 2 applied to pixel p 2 during intermediate display are also equal , and thus the difference in brightness described with reference to fig1 can be eliminated . note that , for the purpose of facilitating understanding of this second embodiment of the present invention , only the cases of black and white display were described , but the present invention is also capable of equalizing the i - v characteristic shift of non - linear elements under all display conditions . this means that the phenomenon of afterimages can be reduced , irrespective of the type of display . a third embodiment of the present invention is an improvement to the drive method used by the liquid crystal display device of fig1 . fig2 is a timing chart of the y driver which is necessary for carrying out a third embodiment of the present invention . note that the dy , yscl , fry , c 1 , and cn signals are the same as those that have already been described with reference to fig5 . y driver outputs the selection voltge signal vs as the output vn when the selection signal cn is 1 in the same way , but in order to carry out this third embodiment , the phase relationship between the selection signal cn and the ac inversion signal fry is changed . the example shown in fig2 differs from that of the first embodiment shown in fig1 in that the switching of fry is set to be at the center of the period during which cn is 1 , so the duty ratio of yn is uniform . note that this duty ratio can be freely selected by changing the phases of cn and fry . the actual drive created by combining the operation of the above - described y driver and the x driver will now be described with reference to fig2 . fig2 shows the waveforms of signals applied to the pixel that is the mth pixel in the horizontal direction and the nth pixel in the vertical direction , in the liquid crystal panel 115 of fig1 , in the same manner as already described for fig1 . the column electrode signal xm sequentially samples the video signal in the a / d converter 120 and outputs von and voff periods based on that data . in this third embodiment , one horizontal scanning period is divided into two parts , ta and tb , with the selection data for the initial period ta being the complement of the data of the ending period tb . since the ac inversion signal frx switches within one horizontal scanning period , the data of the initial part of the actual column electrode signal is symmetrical with the ending data about the axis of this switch in frx . therefore , the potential von of the column electrode signal xm in the write period tb is va in the waveform shown in fig2 so that a relatively large voltage is applied to the pixel in connection with the polarity of the scanning signal in the period tb , but the column electrode signal xm has a potential von of a substantially equal pulse width in each of the periods ta and tb . the description of this embodiment deals with the case in which ta = tb ( and thus ta = tb = ½ horizontal scanning period ), but the drive of the third embodiment of the present invention can equally well be applied to the case in which ta ≠ tb . the row electrode signal yn is the signal described with reference to fig2 . since the polarity of the row electrode signal yn inverts hugely in one horizontal scanning period , the polarity of the difference signal xm − yn between the column electrode signal xm and the row electrode signal yn , both of which are actually applied to the non - linear element 114 and liquid crystal layer 113 also changes greatly between positive and negative , as shown at the bottom of fig2 . it can be seen from this figure that the pixel is selected twice , i . e ., in two selection periods , ta and tb , within one horizontal scanning period . in fig2 too , it is the selection of the ending period tb that determines the display gradation ( in the example on the right - hand side of fig2 , this is a write at positive polarity side ). this means that , with the drive of fig2 , a display gradation ( or rather , the root - mean - square value actually applied to the liquid crystal layer 113 ) has the same effect as that of fig1 . in the drive example in accordance with the third embodiment of the present invention as well , the compensatory selection in the initial period ta is the complement of the actual selection in the ending period tb . when the mode of display is the negative display , the left - hand side of fig2 shows an example where the pixel shows an intermediate display close to white . in the selection of the ending period tb , the ratio of von to voff is comparatively large and thus a large root - mean - square value is applied to the liquid crystal layer 113 of fig1 . however , since the complementary data described above is selected in the selection in the initial period ta , a wide pulse of the same potential as the potential von in the ending period tb functions as the voff potential when it is applied to the pixel , so that in effect the selection is such that the ratio with von is small . conversely , in the example shown on the right - hand side of fig2 , where the pixels &# 39 ; showing is close to black , the ratio of von to voff in the actual selection in the ending part is small and thus a comparatively small root - mean - square value is applied to the liquid crystal layer 113 . however , for the same reason as described above , the selection in the compensatory selection of the ending part is in effect at a ratio of von to voff that is large . to summarize the above description : in the selection for an intermediate display close to white where a large root - mean - square value is required for the liquid crystal layer , the root - mean - square value of the compensatory selection of the initial part is small . conversely , for a selection for an intermediate display close to black , the root - mean - square value of the compensatory selection of the initial part is large . in other words , in order to compensate in the compensatory selection of the initial part for the actual selection in the ending part that is necessary for the actual display , the root - mean - square values applied to the non - linear element 114 that is changing from white to black can be made to be substantially uniform . this operation enables a reduction in afterimages caused by i - v characteristic shift in the non - linear elements . to be precise , if the effective voltage vmw for white display and the effective voltage vmb for black display that are applied to the non - linear element are made the same , the i - v characteristic shift of the non - linear element can be made uniform , and the phenomenon of afterimages caused by i - v characteristic shift can be eliminated . writing the conditions of fig2 as an equation gives equation 3 , in the same way as with the first and second embodiments . therefore , it is best to ensure that the values of the periods ta and tb of the compensatory selection and the actual selection satisfy this equation . note that if ta = tona + toffa and tb = tonb + toffb and the ratio tona / toffa is substantially the reciprocal of tonb / toffb , the data of the compensatory selection is the complement of the data of the actual selection . in general , in the beginning of the compensatory selection period , the potential applied to the non - linear element changes to the compensatory selection potential from that applied in the non - selection period . on the left - hand side of fig2 , this potential goes from − 2va to −( vp − va ); on the right - hand side , it goes from 0 to −( vp + va ). in the beginning of the actual selection , however , the potential applied to the non - linear element changes much more , from the compensatory selection potential to the actual selection potential . on the left - hand side of fig2 , this potential goes from −( vp − va ) to ( vp + va ); on the right - hand side , it goes from −( vp + va ) to ( vp − va ). therefore , a larger potential is applied to the non - linear element for the actual selection , and consequently ta & gt ; tb . the enabling of a dramatic decrease in afterimages due to i - v characteristic shift of the non - linear element will now be described with reference to the example of fig2 . in the same way as described with reference to fig1 , the signal applied to pixel p 1 ( in other words , xm 1 − yn ) and the signal applied to pixel p 2 ( in other words , xm 2 − yn ) are shown in fig2 . pixel p 1 shows a black display and pixel p 2 shows a white display . when the display is switched to an intermediate display at this point , the principle described above dictates that the effective voltage vmsb applied to pixel p 1 and the effective voltage vmsw applied to pixel p 2 are equal , so the magnitude of i - v characteristic shift in these non - linear elements is similarly equal . therefore , the effective voltage s 1 applied to pixel p 1 and the effective voltage s 2 applied to pixel p 2 during intermediate display are also equal , and thus the difference in brightness described with reference to fig1 can be eliminated . note that , for the purpose of facilitating understanding of this third embodiment of the present invention , only the cases of black and white display were described , but the third embodiment of the present invention is also capable of equalizing the i - v characteristic shift of non - linear elements under all display conditions . this means that the phenomenon of afterimages can be reduced , irrespective of the type of display . a fourth embodiment of the present invention concerns a case where the signal waveform of the difference signal xm − yn is changed as shown in fig2 by changing the waveform of the column electrode signal xm in fig2 , which is the timing chart of the third embodiment in the third embodiment of the present invention , the data of the initial period ta which is the compensatory selection is symmetrical with the data of the ending period tb which is the actual selection , about the axis of the switch in frx , as shown in the column electrode signal xm of fig2 . in this fourth embodiment of the present invention , the same data is temporally compressed into , for example , half the horizontal scanning period and is output twice in succession within one horizontal scanning period , as shown by the column electrode signal xm of fig2 . as a result , in contrast to the difference signal xm − yn of the third embodiment shown in fig2 , in which the period tona that governs von of the compensatory selection is on the right of the period ta of the compensatory selection , that of the fourth embodiment shown in fig2 is such that the period tona that governs von of the compensatory selection is on the left of the period ta . a configuration example of the x driver that outputs the column electrode signal xm shown in fig2 is shown in fig2 . this figure shows a drive circuit that supplies an m - bit video data signal to each of n data lines . in this figure , reference number 300 denotes a data bus that supplies the m - bit video data signal which inverts in n cycles within one field , as shown by 421 in fig2 . the m - bit video data signal is written to first memories 311 to 315 corresponding to addresses determined in accordance with the outputs of n - stage shift registers 301 to 305 . reference numbers 351 to 355 in fig2 denote output signals from the shift registers 301 to 305 , respectively . the output signals 351 to 355 are usually at 0 but become 1 once only within one field to write the contents of the data bus 300 to the corresponding first memories 311 to 315 . the timing chart of fig2 illustrates this state , where the output signals of the shift registers 301 to 305 are shown as reference numbers 401 to 405 , respectively . the contents of the data stored in each of the first memories 311 to 315 are shown as reference numbers 411 to 415 , respectively . note that the shading in fig2 denotes an undetermined status . in fig2 and fig2 , the video data signal on the data bus 300 is written to memory 311 at a timing t 1 , to memory 312 at a timing t 2 , and to memory 313 at a timing t 3 . thereafter , video data is written to each memory in turn until data is written to the final - stage memory 315 at a timing tn , which completes the operation of writing video data to memory in this field . this one field of video data is equivalent to the video data for one scan line . in fig2 , a latch pulse ( lp ) 360 is input to second memories 321 to 325 . this latch pulse 360 acts to transfer the data that is in the first memories 311 to 315 to the second memories 321 to 325 . the signal waveform of the latch pulse 360 is shown as reference number 422 in fig2 . during the time that this latch pulse 422 is high level , the data in the first memories 311 to 315 is written in a batch to the second memories 321 to 325 . during the time it is low level , the data in the second memories 321 to 325 is held stable , as shown by data 423 in fig2 . the operation that generates the column electrode signal xm shown in fig2 , based on the data in the second memories 321 to 325 , will now be described with reference to the timing chart of fig2 . the second memories 321 to 325 each output m - bit data signals 371 to 375 , as shown in fig2 . these m - bit data signals 371 to 375 and a basic pulse train 361 ( which form constituent elements of a grayscale signal ) are combined by grayscale signal generation circuits 331 to 335 to generate individual - stage grayscale signals 381 to 385 ( in other words , the column electrode signal xm ). in this case , the basic pulse train 361 comprises a reset signal res and a gcp signal formed of , for example , 2 m pulses of a different pulse width , as shown in fig2 . the reset signal res has a pulse that goes high at the initial - period position and final - period position of the horizontal scanning period , in the same manner as the latch pulse 422 , as shown in fig2 , and it also has a pulse at the central position of the horizontal scanning period . the gcp signal are output in succession in one horizontal scanning period as two identical signals , each compressed into the time of half the horizontal scanning period . the reset signal res and the gcp signal compound the outputs from the second memories 321 to 325 , as shown in fig2 , the signal 381 to 385 can be generated in the form of a uniform waveform which reflects the grayscale data is output sequentially within the horizontal scanning period so that the signals 381 to 385 can be generated . note that these grayscale signal generation circuits 331 to 335 can invert the polarity of the data 381 to 385 within the horizontal scanning period , based on the polarity inversion signal ( fr ). the outputs 381 to 385 of the grayscale signal generation circuits 331 to 335 are input to liquid crystal drive circuits 341 to 345 . these liquid crystal drive circuits 341 to 345 generate liquid crystal drive signals 391 to 395 ( i . e ., the column electrode signal xm ) of levels that are shifted from the grayscale signals 381 to 385 in accordance with a voltage level 362 ( i . e ., va or − va ) that turns the liquid crystal on and a voltage level 363 ( i . e ., − va or va ) that turns the liquid crystal off . the x driver that outputs the column electrode signal xm shown in fig2 can be configured as shown in fig3 . in this figure , a bidirectional shift register 601 , a first latch 602 , a second latch 604 , a decoder 605 , a level shifter 607 , and an lcd driver 608 correspond to the shift registers 301 to 305 , the first memories 311 to 315 , the second memories 321 to 325 , the grayscale signal generation circuits 331 to 335 , and the liquid crystal drive circuits 341 to 345 , respectively , of fig2 . in fig3 , an enable controller 600 controls the bidirectional shift register 601 and a data controller 604 at the timing of a signal such as the latch pulse lp , to implement the data transfer of fig2 . the circuitry of fig3 differs from that of fig2 in that gcp is not a signal having a 2 m pulse width , it is a signal having a pulse at a 2 m th position in accordance with grayscale value , and in that the decoder 605 that inputs the gcp signal through a grayscale controller 606 detects data 371 to 375 output from the second latch 604 together with the gcp signal to generate the grayscale signals 381 to 385 shown in fig2 . except for these points , the operation of the circuit of fig3 is the same as that shown in the timing chart of fig2 . in this way , the fourth embodiment of the present invention can easily generate the column electrode signal xm that is configured by outputting a waveform which reflects the grayscale data twice in succession within one horizontal scanning period , using the relatively simple drive circuit shown in either fig2 or fig3 . it can also shape the difference signal xm − yn of the column electrode signal xm and the row electrode signal yn ( shown in fig2 ) in such a manner that the period tona for von in the compensatory period ta is on the left of the compensatory period ta . note that in this fourth embodiment too , the difference signal xm − yn shown in fig2 divides the horizontal scanning period into two periods , ta and tb , and the initial - part and ending - part data is in a complementary relationship . this enables a reduction in afterimages caused by i - v characteristic shift in the non - linear elements , in the same way as in the third embodiment . the drive circuit shown in fig2 and used in this fourth embodiment is simple to construct , as can easily be understood by a comparison with the drive circuit of the third embodiment for generating the column electrode signal xm shown in fig2 . the waveform of the column electrode signal xm used in the third embodiment is shown in fig2 a . it reflects the grayscale data , but it has also been made symmetrical about the boundary between the periods ta and tb . an example of the configuration of the drive circuit for generating the waveform of fig2 a is shown in fig2 b . in this case , a comparatively large memory such as a first - in , first - out ( fifo ) memory 501 is necessary . the video signal that is the input signal to the fifo memory 501 is shown in fig2 c , and the output signal from the fifo memory 501 is shown in fig2 d . the read clock of the fifo memory 501 is set to be at twice the speed of the write clock thereof . as a result , the output signal from the fifo memory 501 has a timing that is delayed by half the horizontal scanning period with respect to the input signal shown in fig2 c , and the video signal of fig2 c is compressed to half along the time axis so that the same signal waveform is output twice in succession . the output from the fifo memory 501 is input to an x driver 503 via a signal processing circuit 502 that processes signal on the basis of an ac inversion signal frx , so that the symmetrical pulse waveform shown in fig2 a can be output as the column electrode signal xm . a fifth embodiment of the present invention concerns an improvement which ensures that any noise caused by the difference signal xm − yn of the first to fourth embodiments ( or rather , by the huge change in potential that occurs at the boundary between the periods ta and tb ) does not appear on the liquid crystal panel 115 . at the boundary between the periods ta and tb in the difference signal xm − yn , the voltage experiences a huge shift from a negative potential to a positive one , as shown in fig3 . it is feared that this huge potential difference generated in the liquid crystal display device will be superimposed as noise in the video circuitry of the previous stage , and also in the tuner circuitry and antenna of earlier stages , and will eventually appear as noise on the liquid crystal screen . it is possible to remove this noise by providing an exclusion circuit in the video circuitry , for example , but this would make the structure complicated . the fifth embodiment of the present invention solves this problem by placing the compensatory selection period ta of the difference signal xm − yn so that it is included within the flyback period of the video signal . in terms of the relationship between the compensatory selection period ta and the horizontal scanning period ( ta + tb ), this can be expressed by : even more preferably , it is best if ta is no more than 15 % of ( ta + tb ), to ensure that the width of the period ta substantially matches the width of the flyback signal . as shown in fig3 , the video signal and the difference signal xm − yn are synchronized . therefore , by making sure that the above equation is satisfied , the compensatory selection pulse ( i . e ., the compensatory selection period ta ) within the difference signal can be set to substantially correspond to the flyback signal of the video signal along the time axis . then , even if noise caused by the huge potential difference within the difference signal xm − yn is superimposed on the video signal , it is superimposed on the signal during the flyback period . the signal within this flyback period is not displayed on the liquid crystal screen , and thus it does not appear as noise on the liquid crystal screen . a sixth embodiment of the present invention concerns an improvement to the drive waveform of the column electrode signal xm , whereby the voltages applied to the two ends of the non - linear element and the liquid crystal layer are made even larger during the compensatory selection than during the actual selection . an improved version of the column electrode signal xm of fig2 , which shows the waveforms of the fourth embodiment , is shown in fig3 . in this figure , the reference potentials vb and − vb during the compensatory selection are set with respect to reference potentials va and − va of the column electrode signal xm during the actual selection such that | vb |& gt ;| va |. in the example shown in fig3 , even when the amplitude of the row electrode signal yn changes by 2 × vp , the potential of the difference signal xm − yn during the compensatory selection is made relatively greater than that during the actual selection . similarly , improved versions of the column electrode signal xm and row electrode signal yn of fig1 , which shows the waveforms of the second embodiment , are shown in fig3 . in this figure too , the reference potentials vb and − vb during the compensatory selection are set with respect to reference potentials va and − va of the column electrode signal xm during the actual selection such that | vb |& gt ;| va |. the description based on fig3 refers to white display ( corresponding to the left - hand side of the figure ). in order to show a white display by the pixels , the write potential is at a maximum of | vp + va | during the actual selection . in this case , the potential of the compensating voltage is | vr − vb | which is the minimum potential , because it is necessary to write the complementary data to the selection data at the compensatory selection . conversely , when the pixels show a black display ( corresponding to the right - hand side of the figure ), the write potential for the actual selection is at a minimum at | vp − va | and the compensatory selection is at a maximum potential of | vr + vb |. therefore , when white is selected , a large potential is applied to the non - linear element during the actual selection , but the non - linear element is subjected to only a small potential in the preceding compensatory selection . conversely , when black is selected , the potential in the actual selection is small , but a large potential is applied to the non - linear element during the compensatory selection . in other words , this means that the total potential applied to the non - linear element can be made the same , regardless of whether black or white is selected . an example of the configuration of the drive circuit on the row electrode side is shown in fig3 . in this figure , the drive circuit is provided with a first power supply 701 for setting the reference voltage va during the actual selection as the power voltage for the x driver 700 , and a second power supply 702 for setting the reference voltage vb during the compensatory selection . the configuration is such that power is supplied to the x driver 700 by the switching of the two supplies by a switch 703 that operates based on the ac inversion signal fr . in this case , the configuration could be such that relatively low voltages are supplied , such as about 5 v by the first power supply 701 and about 6 v by the second power supply 702 . in contrast , when the potential during the compensatory selection of the row electrode signal yn is set to be greater than that during the actual selection , as in the second embodiment of the present invention , the power supply voltage connected to the y driver must be large . this is particularly necessary when an mim element is used as the non - linear element , because an mim element needs a much larger voltage such as 30 to 40 v , and setting an even larger voltage on top of that will increase the load . it is possible to enable a liquid crystal drive circuit that uses an mim element to obtain such a large voltage as 30 to 40 v by swinging a lower voltage to generate a large voltage , but it is difficult to accurately generate the potential vr for the complementary selection by a voltage swing with respect to the potential vp necessary during the actual selection shown in fig1 . therefore , an x driver that can set a difference signal which has a larger potential in the compensatory selection than that in the actual selection can be formed simply by adding a power source of a relatively low voltage , and thus is it possible to accurately set a high voltage , with a drive circuit of a simple configuration . note that the first to sixth embodiments of the present invention have been described as having compensatory selection data in a period ta and actual selection data in a period tb , obtained by a difference signal xm − yn , which are in a mutually complementary relationship , but the present invention is not limited thereto . for instance , the complementary relationship need not hold , so long as the relationship is such that , when the data write charge voltage that charges the liquid crystal layer 113 during the actual selection is large , the compensatory charge voltage applied to the liquid crystal layer 113 during the compensatory selection is small and , conversely , when the data write charge voltage is small , the compensatory charge voltage is large . so long as this relationship between the actual selection data and the compensatory selection data holds , the afterimage phenomenon can be controlled . in addition , the first to sixth embodiments of the present invention can also be carried out with polarity inversion techniques at every line that drive the device in such a manner that the polarity of the voltage charged into the liquid crystal layers of pixels in odd - numbered frames , for instance , is different from the polarity of the voltage that charges the liquid crystal layers of pixels in even - numbered frames . a plan view of the non - linear element ( denoted by reference number 114 in fig1 and fig1 ) of one pixel in a liquid crystal panel that uses a seventh embodiment of the present invention is shown in fig3 . in this figure , an mim element using tantalum - tantalum oxide - chromium as materials is used as the non - linear element , and reference number 801 denotes a tantalum covered with tantalum oxide that also serves as a column electrode . reference number 802 denotes chromium patterns . an mim element is formed at an intersection between chromium patterns 802 and tantalum 801 . reference number 803 denotes a transparent ito pattern that forms a pixel electrode . fig3 is a cross - sectional view through the structure of the mim element , taken along the dot - dash line 804 in fig3 . reference number 901 denotes a transparent substrate , reference number 902 denotes a tantalum portion , and reference number 903 denotes a tantalum oxide portion . the method of fabricating the mim element of this configuration will now be described . a tantalum layer is formed on the transparent substrate by sputtering , and this layer is patterned to form a tantalum electrode that will be the column electrode . this tantalum electrode is subjected to anodic oxidization to cover the surface thereof with tantalum oxide . a diluted aqueous solution of phosphoric acid is used as the electrolyte for the anodic oxidization . an oxide layer of a uniform thickness is obtained by initially controlling the current , then by applying a constant voltage . subsequently , a chromium layer is sputtered and patterned , then ito that is to form a transparent pixel electrode is also sputtered and patterned thereon . this enables the formation of an electrode substrate having mim element . a liquid crystal panel can be formed by pasting this substrate together with a substrate formed of a resistance electrode , with a liquid crystal inserted into a gap therebetween . fig3 is a graph of measurements done on the magnitude of afterimages in the present embodiment these measurements were done after the window display of fig8 had been left on the liquid crystal panel for a fixed time then the entire panel was switched to the uniform display shown in fig9 . this graph shows variations in brightness ratio for the points p 1 and p 2 in fig9 . elapsed time after the display is switched to the uniform display is shown along the x - axis on a logarithmic scale , and the y - axis shows rδt when the brightnesses of the points p 1 and p 2 are tp 1 and tp 2 , respectively , where rδt expresses the degree of brightness ratio and is defined as : if a prior art drive method is defined as a , the drive method described as the third embodiment of the present invention is a , a device using a liquid crystal panel formed by a prior art anodic oxidization method is b , and a device using a liquid crystal panel formed by the anodic oxidization method of the seventh embodiment is b , the change in brightness ratio obtained by a combination of a and b is shown as line 1 , that for a and b is line 2 , that for a and b is line 3 , and that for a and b ( completely in accordance with the present invention ) is line 4 . results obtained by comparison with functional tests show that , if the brightness ratio rδt is in general initially 8 % or less , afterimages cannot be discerned . actual tests with display devices in accordance with embodiments of the present invention in comparison with prior art devices have proved that , provided fixed patterns were not held on display for excessively long times , afterimages could not be discerned . by forming the insulator layer that will become a non - linear resistance element by anodic oxidization using an electrolytic liquid that includes phosphorus , it is possible to greatly reduce the magnitude of the i - v characteristic shift in comparison with a prior art non - linear element . this phenomenon has been confirmed by experimental results , but the mechanism thereof has not yet been clarified . it is assumed that perhaps the inclusion of phosphorus in an oxide film stabilizes the ranking of impurities existing within the film , and thus the current flowing therethrough is also stabilized by the poole - frenkel effect or schottky effect . note that the insulator layer described above would have the same effect if it is the insulator layer of an mis element . note also that if one of the metal layers of an mim element is formed as transparent electrode layer , it can also be used as a transparent electrode of the liquid crystal panel .