The triangle method for finding the corner of the L-curve

被引：101

作者：

Castellanos, JL ^{[1
]}

Gómez, S ^{[1
]}

Guerra, V ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, IIMAS, Mexico City 01000, DF, Mexico

来源：

APPLIED NUMERICAL MATHEMATICS | 2002年 / 43卷 / 04期

关键词：

CG-method; regularization; L-curve; ill-conditioned matrices; systems of linear equations;

D O I：

10.1016/S0168-9274(01)00179-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Conjugate Gradient Method (CG) has an intrinsic regularization property when applied to systems of linear equations with ill-conditioned matrices. This regularization property is specially useful when either the right-hand side or the coefficient matrix, or both are given with errors. The regularization parameter is the iteration number, and in order to find this parameter, the L-curve is used. Here we present a novel method to find the corner of the L-curve, that determines the regularizing iteration number. Numerical results on the collection of test problems [SIAM J. Sci. Comput. 16 (1995) 506-512] are given to illustrate the potentiality of the method. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.

引用

页码：359 / 373

页数：15

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