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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Vydáno v:SIAM journal on scientific and statistical computing Ročník 4; číslo 2; s. 164 - 176
Hlavní autor: Varah, J. M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.06.1983
Témata:
Decomposition
Integral equations
Laplace transforms
Noise
Regularization methods
ISSN:0196-5204, 1064-8275, 2168-3417, 1095-7197
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0904012