M. A. Krasnosel'skii Theorem and Iterative Methods for Solving Ill-Posed Linear Problems
with a Self-Adjoint Operator

Oleg Matysik; Petr Zabreiko

doi:10.1515/cmam-2015-0016

Published by De Gruyter June 6, 2015

M. A. Krasnosel'skii Theorem and Iterative Methods for Solving Ill-Posed Linear Problems with a Self-Adjoint Operator

Oleg Matysik and Petr Zabreiko

From the journal Computational Methods in Applied Mathematics

https://doi.org/10.1515/cmam-2015-0016

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Abstract

The paper deals with iterative methods for solving linear operator equations x=Bx+f and Ax=f with self-adjoint operators in Hilbert space X in the critical case when ρ(B)=1 and 0∈SpA. The results obtained are based on a theorem by M. A. Krasnosel'skii on the convergence of the successive approximations, their modifications and refinements.

Keywords: Ill-Posed Linear Problems; Method of Successive Approximations; Spectrum of Operator; Errors; Residuals and Corrections; Weakened Norms; Orthogonal Projection; Convergence and Convergence Rate of Approximations

MSC: 47A52; 65F22; 65Q30

Received: 2015-2-2

Revised: 2015-4-21

Accepted: 2015-5-20

Published Online: 2015-6-6

Published in Print: 2015-7-1

M. A. Krasnosel'skii Theorem and Iterative Methods for Solving Ill-Posed Linear Problems with a Self-Adjoint Operator

Abstract

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