Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problems

被引：15

作者：

Chu, Delin ^{[4
]}

Lin, Lijing ^{[3
]}

Tan, Roger C. E. ^{[4
]}

Wei, Yimin ^{[1
,2
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China

[3] Fudan Univ, Inst Math Sci, Shanghai 200433, Peoples R China

[4] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

来源：

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2011年 / 18卷 / 01期

基金：

中国国家自然科学基金;

关键词：

linear least squares; condition number; Tikhonov regularization; perturbation; LINEAR LEAST-SQUARES; SINGULAR VALUE DECOMPOSITION; NUMERICAL SOLUTION; COMPONENTWISE; BOUNDS;

D O I：

10.1002/nla.702

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

One of the most successful methods for solving the least-squares problem min(x) parallel to A(x) - b parallel to(2) with a highly ill-conditioned or rank deficient coefficient matrix A is the method of Tikhonov regularization. In this paper, we derive the normwise, mixed and componentwise condition numbers and componentwise perturbation bounds for the Tikhonov regularization. Our results are sharper than the known results. Some numerical examples are given to illustrate our results. Copyright (C) 2010 John Wiley & Sons, Ltd.

引用

页码：87 / 103

页数：17

共 43 条

[31]

HIGHAM NJ, 1994, P S APPL MATH, V48, P49

[32] A unified theory of conditioning for linear least squares and Tikhonov regularization solutions [J].

Malyshev, AN .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 24 (04) :1186-1196

[33]

Morozov V.A., 1984, METHODS SOLVING INCO

[34] A TECHNIQUE FOR NUMERICAL SOLUTION OF CERTAIN INTEGRAL EQUATIONS OF FIRST KIND [J].

PHILLIPS, DL .

JOURNAL OF THE ACM, 1962, 9 (01) :84-&

[35]

RICE JR, 1996, SIAM J NUMER ANAL, V3, P175

[36] NEW CONDITION NUMBERS FOR MATRICES AND LINEAR-SYSTEMS [J].

ROHN, J .

COMPUTING, 1989, 41 (1-2) :167-169

[37] IMPROVEMENT OF RESOLUTION OF AN INSTRUMENT BY NUMERICAL SOLUTION OF AN INTEGRAL-EQUATION [J].

SHAW, CB .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1972, 37 (01) :83-&

[38]

Skeel R., 1979, J ASS COMPUT MATH, V26, P167

[39]

TIKHONOV AN, 1963, DOKL AKAD NAUK SSSR+, V151, P501

[40] GENERALIZING SINGULAR VALUE DECOMPOSITION [J].

VANLOAN, CF .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1976, 13 (01) :76-83

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