Generalized approximate inverse preconditioners for least squares problems

被引：0
作者：
Xiaoke Cui
Ken Hayami
机构：
[1] The Graduate University for Advanced Studies (Sokendai),Department of Informatics, School of Multidisciplinary Sciences
[2] National Institute of Informatics,Principles of Informatics Research Division
来源：
Japan Journal of Industrial and Applied Mathematics | 2009年 / 26卷
关键词：
approximate inverse; least squares problem; preconditioning; rectangular matrix;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper is concerned with a new approach for preconditioning large sparse least squares problems. Based on the idea of the approximate inverse preconditioner, which was originally developed for square matrices, we construct a generalized approximate inverse (GAINV)M which approximately minimizes ∥/ −M A∥F or ∥I −AM∥F. Then, we also discuss the theoretical issues such as the equivalence between the original least squares problem and the preconditioned problem. Finally, numerical experiments on problems from Matrix Market collection and random matrices show that although the preconditioning is expensive, it pays off in certain cases.
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