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Kernel polynomials for the solution of indefinite and ill-posed problems

Content Provider	Springer Nature Link
Author	Frankenberger, Harald Hanke, Martin
Copyright Year	2000
Abstract	We introduce a new family of semiiterative schemes for the solution of ill-posed linear equations with selfadjoint and indefinite operators. These schemes avoid the normal equation system and thus benefit directly from the structure of the problem. As input our method requires an enclosing interval of the spectrum of the indefinite operator, based on some a priori knowledge. In particular, for positive operators the schemes are mathematically equivalent to the so-called ν-methods of Brakhage. In a way, they can therefore be seen as appropriate extensions of the ν-methods to the indefinite case. This extension is achieved by substituting the orthogonal polynomials employed by Brakhage in the definition of the ν-methods by appropriate kernel polynomials. We determine the rate of convergence of the new methods and establish their regularizing properties.
Starting Page	197
Ending Page	212
Page Count	16
File Format	PDF
ISSN	10171398
Journal	Numerical Algorithms
Volume Number	25
Issue Number	1-4
e-ISSN	15729265
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2000-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theory of Computation Numeric Computing Mathematics Algebra Algorithms
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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