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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Baghdad, College of Science for Women
2016-03-01
|
| Series: | مجلة بغداد للعلوم |
| Subjects: | |
| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2154 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
|---|---|
| ISSN: | 2078-8665 2411-7986 |