A Note on the Perturbation of arithmetic expressions | ||
| Baghdad Science Journal | ||
| Article 1, Volume 13, Issue 1, February 2016, Pages 190-197 | ||
| Author | ||
| Shawki A.M. Abbas | ||
| Abstract | ||
| In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under; • Approximations in "built-in" functions. • Rounding errors in arithmetic floating-point operations. • Perturbations of data. The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a priori and a posteriori error analysis. | ||
| Keywords | ||
| built in function; Rounding errors; perturbations data; Boundary Value Problem | ||
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