Pitfalls in the Numerical Solution of Linear Ill-Posed Problems

Very special computational difficulties arise when we attempt to solve linear systems arising from integral equations of the first kind. We examine here existence and uniqueness questions associated with so-called reasonable solutions for such problems, and present results using the best-known metho...

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Bibliographic Details
Published in:SIAM journal on scientific and statistical computing Vol. 4; no. 2; pp. 164 - 176
Main Author: Varah, J. M.
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.06.1983
Subjects:
Decomposition
Integral equations
Laplace transforms
Noise
Regularization methods
ISSN:0196-5204, 1064-8275, 2168-3417, 1095-7197
Online Access:Get full text
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Summary:Very special computational difficulties arise when we attempt to solve linear systems arising from integral equations of the first kind. We examine here existence and uniqueness questions associated with so-called reasonable solutions for such problems, and present results using the best-known methods on inverse Laplace transform problems. We also discuss the choice of free parameters occurring in these methods from the same point of view.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0904012