# Discrepancy of an approximation

From Encyclopedia of Mathematics

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