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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Discrepancy_of_an_approximation&oldid=14211
Discrepancy of an approximation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Discrepancy_of_an_approximation&oldid=14211
This article was adapted from an original article by N.S. Bakhvalov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article