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.
Keywords
built in function, Rounding errors, perturbations data, boundary value problem.
Article Type
Article
How to Cite this Article
Abbas, Shawki A.M.
(2016)
"A Note on the Perturbation of arithmetic expressions,"
Baghdad Science Journal: Vol. 13:
Iss.
1, Article 21.
DOI: https://doi.org/10.21123/bsj.2016.13.1.0190