A general heuristic for choosing the regularization parameter in ill-posed problems

被引：83

作者：

Hanke, M ^{[1
]}

Raus, T ^{[1
]}

机构：

[1] TARTU STATE UNIV,DEPT MATH,EE-2400 TARTU,ESTONIA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 1996年 / 17卷 / 04期

关键词：

ill-posed problems; Tikhonov regularization; iterative regularization; conjugate gradients; a posteriori parameter choice;

D O I：

10.1137/0917062

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a variety of regularization methods, including Tikhonov regularization, Landweber iteration, nu-method iteration, and the method of conjugate gradients, rye develop and illustrate a heuristic for choosing an appropriate regularization parameter. Our choice requires no particular a priori knowledge, since the parameter is determined from computable information only. However, if an estimation for the noise level in the data is at hand, then this can be used as a justification. In contrast to known parameter choice heuristics, a posteriori error estimates for the computed approximations can be given. Numerical examples show that the new parameter choice rules are promising alternatives to known parameter choice rules.

引用

页码：956 / 972

页数：17

共 22 条

[11]

Hanke M., 1995, Conjugate gradient type methods for ill-posed problems

[12] ANALYSIS OF DISCRETE ILL-POSED PROBLEMS BY MEANS OF THE L-CURVE [J].

HANSEN, PC .

SIAM REVIEW, 1992, 34 (04) :561-580

[13]

LEONOV AS, 1978, SOV MATH DOKL, V119, P537

[14]

Louis A K., 1989, Inverse und schlecht gestellte Probleme

[15] THE REGULARIZING PROPERTIES OF THE ADJOINT GRADIENT-METHOD IN ILL-POSED PROBLEMS [J].

NEMIROVSKII, AS .

USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1986, 26 (02) :7-16

[16]

NEUBAUER A, IN PRESS SIAM J NUME

[17]

RAUS T, 1985, UCHEN ZAP TARTU GOS, V715, P12

[18]

Tikhonov A.N., 1965, USSR COMP MATH MATH, V5, P93, DOI DOI 10.1016/0041-5553(65)90150-3

[19]

Vainikko GM., 1986, ITERATION PROCEDURES

[20]

VAINIKKO GM, 1980, AUTOMAT REM CONTR, V40, P356

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