On the Numerical Solution of Ill-Conditioned Linear Systems with Applications to Ill-Posed Problems

We consider the solution of ill-conditioned linear systems using the singular value decomposition, and show how this can improve the accuracy of the computed solution for certain kinds of right-hand sides. Then we indicate how this technique is especially appropriate for some classical ill-posed pro...

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Bibliographic Details
Published in:SIAM journal on numerical analysis Vol. 10; no. 2; pp. 257 - 267
Main Author: Varah, J. M.
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.04.1973
Subjects:
Computer science
Decomposition
Differential equations
Eigenvalues
Eigenvectors
Error rates
Ill posed problems
Laplace transformation
Laplace transforms
Least squares
Linear systems
Mathematics
Matrices
ISSN:0036-1429, 1095-7170
Online Access:Get full text
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Summary:We consider the solution of ill-conditioned linear systems using the singular value decomposition, and show how this can improve the accuracy of the computed solution for certain kinds of right-hand sides. Then we indicate how this technique is especially appropriate for some classical ill-posed problems of mathematical physics.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0036-1429
1095-7170
DOI:10.1137/0710025