Trust-region and other regularisations of linear least-squares problems

被引：23

作者：

Cartis, C. ^{[1
]}

Gould, N. I. M. ^{[2
]}

Toint, P. L. ^{[3
]}

机构：

[1] Univ Edinburgh, Sch Math, Edinburgh EH9 3JZ, Midlothian, Scotland

[2] Rutherford Appleton Lab, Computat Sci & Engn Dept, Chilton OX11 0QX, Oxon, England

[3] Univ Namur, Fac Univ Notre Dame Paix, Dept Math, B-5000 Namur, Belgium

来源：

BIT NUMERICAL MATHEMATICS | 2009年 / 49卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Linear least-squares; Regularisation; Trust-region; Secular equation; ALGORITHM; REGULARIZATION; EQUATIONS; LSQR;

D O I：

10.1007/s10543-008-0206-8

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We consider methods for regularising the least-squares solution of the linear system Ax = b. In particular, we propose iterative methods for solving large problems in which a trust-region bound ||x|| <= Delta is imposed on the size of the solution, and in which the least value of linear combinations of ||Ax - b||(q)(2) and a regularisation term ||x||(2)(p) for various p and q = 1, 2 is sought. In each case, one or more "secular" equations are derived, and fast Newton-like solution procedures are suggested. The resulting algorithms are available as part of the GALAHAD optimization library.

引用

页码：21 / 53

页数：33

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