1. A method for pulling up a single crystal ingot ( 15 ) from a melt ( 12 ) where either a single crystal, poly crystal or both are melted by a heater ( 18 ) in the furnace of a single crystal puller ( 10 ), the method comprising: calculating the axial temperature gradient G at the solid-liquid interface ( 24 ) from the heating value of a heater ( 18 ), the dimensions and physical property values of the interior furnace components and the convection of the melt ( 12 ) before pulling up the single crystal ingot ( 15 ) by the puller ( 10 ) by use of a numerical simulation of synthetic heater transfers and a numerical simulation of melt convection; determining the pulling velocity V of the single crystal ingot ( 15 ) from a value previously experienced of the ratio C=V/G of the pulling velocity V and the axial temperature gradient G of the single crystal ingot ( 15 ) at which the single crystal ingot ( 15 ) becomes defect-free, obtained when the single crystal ingot ( 15 ) was pulled up by a same type of puller as puller ( 10 ), and the axial temperature gradient G calculated by use of the numerical simulation of synthetic heater transfers and the numerical simulation of melt convection; pulling up the single crystal ingot ( 15 ) by puller ( 10 ) at pulling velocity V; roughly measuring the deterioration value of interior partial furnace components that can be measured while the single crystal ingot ( 15 ) is pulled up by the puller ( 10 ) and which the axial temperature gradient G; roughly forecasting the change value of the axial temperature gradient G to the roughly measured deterioration value of the partial furnace interior components roughly measured in the puller ( 10 ) using the numerical simulation of synthetic heater transfers and the numerical simulation of melt convection; and adjusting the pulling velocity V of the single crystal ingot ( 15 ) by the puller ( 10 ) in such a way that the ratio C becomes the value experienced according to the change value of the axial roughly forecasted temperature gradient G in puller ( 10 ).