Quantitative Criterion of Conditioning for Systems of Linear Algebraic Equations

摘要

Conventional conditioning criteria are shown to be invalid for estimating the accuracy of a numerical calculation for systems of linear algebraic equations. A new conditioning criterion is pro- posed, quantitatively describing the actual loss of decimal digits in calculations. The adequacy of this criterion is confirmed by examples of numerical calculations. Conditioning criteria have been obtained for some types of linear systems arising in important applied problems, in particular, in the difference solution of differential or integral equations.