A Note on the Perturbation of arithmetic expressions
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 fu...
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| Format: | Article |
| Language: | Arabic |
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College of Science for Women, University of Baghdad
2016-03-01
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| Series: | Baghdad Science Journal |
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| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2154 |
| Summary: | 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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| ISSN: | 2078-8665 2411-7986 |