A rational Arnoldi approach for ill-conditioned linear systems

被引：8

作者：

Brezinski, C. ^{[2
]}

Novati, P. ^{[1
]}

Redivo-Zaglia, M. ^{[1
]}

机构：

[1] Univ Padua, Dept Pure & Appl Math, I-35121 Padua, Italy

[2] Univ Sci & Technol Lille, Lab Paul Painleve, UMR CNRS 8524, UFR Math Pures & Appl, F-59655 Villeneuve Dascq, France

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2012年 / 236卷 / 08期

关键词：

Ill-conditioned linear systems; Arnoldi algorithm; Matrix function; Tikhonov regularization; APPROXIMATIONS; REGULARIZATION;

D O I：

10.1016/j.cam.2011.09.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a suitable function of matrix. In this sense, the method can be referred to as an iterative refinement process. Numerical experiments arising from integral equations and interpolation theory are presented. Finally, the method is extended to work in connection with the standard Tikhonov regularization with the right-hand side contaminated by noise. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：2063 / 2077

页数：15

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