Dynamical Systems Method for solving Ill-Conditioned Linear Algebraic Systems

被引：7

作者：

Indratno, Sapto W. ^{[1
]}

Ramm, A. G. ^{[1
]}

机构：

[1] Kansas State Univ, Dept Math, Manhattan, KS 66506 USA

来源：

INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS | 2009年 / 2卷 / 04期

关键词：

Hilbert matrix; FIEFK; Fredholm integral equations of the first kind; iterative regularisation; variational regularisation; discrepancy principle; DSM; Dynamical Systems Method;

D O I：

10.1504/IJCSM.2009.030911

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

A new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving Ill-Conditioned Linear Algebraic System (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In this paper a new iterative scheme for solving ICLAS is proposed. This iterative scheme is based on the DSM solution. An a posteriori stopping rules for the proposed method is justified. This paper also gives an a posteriori stopping rule for a modified iterative scheme developed in A.G. Ramm, Jour. Math. Anal. Appl., Vol. 330 (2007), pp. 1338-1346, and proves convergence of the solution obtained by the iterative scheme.

引用

页码：308 / 333

页数：26

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