Computation of Sharp Rigorous Componentwise Error Bounds for the Approximate Solutions of Systems of Linear Equations

Computation of Sharp Rigorous Componentwise Error Bounds for the Approximate Solutions of Systems... This paper is concerned with the problem of verifying the accuracy of approximate solutions of systems of linear equations. Recently, fast algorithms for calculating guaranteed error bounds of computed solutions of systems of linear equations have been proposed using the rounding mode controlled verification method and the residual iterative verification method. In this paper, a new verification method for systems of linear equations is proposed. Using this verification method, componentwise verified error bounds of approximate solutions of systems of linear equations can be calculated. Numerical results are presented to illustrate that it is possible to get very sharp error bounds of computed solutions of systems of linear equations whose coefficient matrices are symmetric and positive definite. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Computation of Sharp Rigorous Componentwise Error Bounds for the Approximate Solutions of Systems of Linear Equations

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1024655416554
Publisher site
See Article on Publisher Site

Abstract

This paper is concerned with the problem of verifying the accuracy of approximate solutions of systems of linear equations. Recently, fast algorithms for calculating guaranteed error bounds of computed solutions of systems of linear equations have been proposed using the rounding mode controlled verification method and the residual iterative verification method. In this paper, a new verification method for systems of linear equations is proposed. Using this verification method, componentwise verified error bounds of approximate solutions of systems of linear equations can be calculated. Numerical results are presented to illustrate that it is possible to get very sharp error bounds of computed solutions of systems of linear equations whose coefficient matrices are symmetric and positive definite.

Journal

Reliable ComputingSpringer Journals

Published: Oct 17, 2004

References

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