The iodine number and the unsaturation number of fats
In order to determine the degree of unsaturation of fats and to study the kinetics of their hydrogenation, it is proposed to use instead of the iodine number an index which is called the unsaturation number and shows the total number of double bonds in 100 molecules of fatty acids.
We present an incremental approach to 2-norm estimation for triangular matrices. Our investigation covers both dense and sparse matrices which can arise for example from a QR, a Cholesky or a LU factorization. If the explicit inverse of a triangular factor is available, as in the case of an implicit version of the LU factorization, we can relate our results to incremental condition estimation (ICE). Incremental norm estimation (INE) extends directly from the dense to the sparse case without needing the modifications that are necessary for the sparse version of ICE. INE can be applied to complement ICE, since the product of the two estimates gives an estimate for the matrix condition number. Furthermore, when applied to matrix inverses, INE can be used as the basis of a rank-revealing factorization.