A Note on the Perturbation of arithmetic expressions

• Main Author: Baghdad Science Journal
• Format: Article
• Language: Arabic
• Published: College of Science for Women, University of Baghdad 2016-03-01
• Series: Baghdad Science Journal
• Subjects: "built in function, Rounding errors, perturbations data, boundary value problem."
• Online Access: http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2154

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.