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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| Language: | English |
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University of Baghdad, College of Science for Women
2016-03-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2154 |
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| author | Baghdad Science Journal |
| author_facet | Baghdad Science Journal |
| author_sort | Baghdad Science Journal |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e6ccda0149d24378b703cefc04e87b5c |
| institution | Matheson Library |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2016-03-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-e6ccda0149d24378b703cefc04e87b5c2025-08-02T22:07:39ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862016-03-0113110.21123/bsj.13.1.190-197A Note on the Perturbation of arithmetic expressionsBaghdad Science JournalIn 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.http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2154"built in function, Rounding errors, perturbations data, boundary value problem." |
| spellingShingle | Baghdad Science Journal A Note on the Perturbation of arithmetic expressions مجلة بغداد للعلوم "built in function, Rounding errors, perturbations data, boundary value problem." |
| title | A Note on the Perturbation of arithmetic expressions |
| title_full | A Note on the Perturbation of arithmetic expressions |
| title_fullStr | A Note on the Perturbation of arithmetic expressions |
| title_full_unstemmed | A Note on the Perturbation of arithmetic expressions |
| title_short | A Note on the Perturbation of arithmetic expressions |
| title_sort | note on the perturbation of arithmetic expressions |
| topic | "built in function, Rounding errors, perturbations data, boundary value problem." |
| url | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2154 |
| work_keys_str_mv | AT baghdadsciencejournal anoteontheperturbationofarithmeticexpressions AT baghdadsciencejournal noteontheperturbationofarithmeticexpressions |