Iterative solution of linear equations with unbounded operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:330

Article

Ramm, A. G.

关键词: iterative methods;    unbounded operators;    linear equations;   

DOI  :  10.1016/j.jmaa.2006.08.066

来源: Elsevier

【 摘 要 】

A convergent iterative process is constructed for solving any solvable linear equation in a Hilbert space, including equations with unbounded, closed, densely defined linear operators. The method is proved to be stable towards small perturbation of the data. Some abstract results are established and used in an analysis of variational regularization method for equations with unbounded linear operators. The dynamical systems method (DSM) is justified for unbounded, closed, densely defined linear operators. The stopping time is chosen by a discrepancy principle. Equations with selfadjoint operators are considered separately. Numerical examples, illustrating the efficiency of the proposed method, are given. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

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