View source for Discrepancy of an approximation

One of the characteristics of the quality of an approximate solution <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033040/d0330401.png" /> of an operator equation <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033040/d0330402.png" /> (e.g. a linear algebraic system, a differential equation). The discrepancy is defined as the quantity <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033040/d0330403.png" /> or a norm of this quantity, e.g., <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033040/d0330404.png" />. If the estimate

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holds, then the error of the solution may be estimated in terms of the discrepancy:

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If no such estimate is available, the discrepancy provides an indirect indication of the quality of the approximate solution.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  I.S. Berezin,   N.P. Zhidkov,   "Computing methods" , Pergamon  (1973)  (Translated from Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  N.S. Bakhvalov,   "Numerical methods: analysis, algebra, ordinary differential equations" , MIR  (1977)  (Translated from Russian)</TD></TR></table>