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Discrepancy of an approximation

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One of the characteristics of the quality of an approximate solution of an operator equation (e.g. a linear algebraic system, a differential equation). The discrepancy is defined as the quantity or a norm of this quantity, e.g., . If the estimate

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

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

References

[1] I.S. Berezin, N.P. Zhidkov, "Computing methods" , Pergamon (1973) (Translated from Russian)
[2] N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from Russian)
How to Cite This Entry:
Discrepancy of an approximation. N.S. Bakhvalov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Discrepancy_of_an_approximation&oldid=14211
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098