A Note on the Perturbation of arithmetic expressions Shawki A.M. Abbas

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Baghdad Science Journal

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.

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Journal BS. A Note on the Perturbation of arithmetic expressions. BSJ [Internet]. 6Mar.2016 [cited 7Aug.2020];13(1):0190. Available from: http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2154
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