On the computation of a truncated SVD of a large linear discrete ill-posed problem

作     者：Onunwor, Enyinda Reichel, Lothar 

作者机构：Kent State Univ Dept Math Sci Kent OH 44242 USA Stark State Coll Dept Math 6200 Frank Ave NW North Canton OH 44720 USA 

出 版 物：《NUMERICAL ALGORITHMS》 (数值算法)

年 卷 期：2017年第75卷第2期

页      面：359-380页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Discrete ill-posed problem Truncated SVD Lanczos method Golub-Kahan bidiagonalization 

摘      要：The singular value decomposition is commonly used to solve linear discrete ill-posed problems of small to moderate size. This decomposition not only can be applied to determine an approximate solution but also provides insight into properties of the problem. However, large-scale problems generally are not solved with the aid of the singular value decomposition, because its computation is considered too expensive. This paper shows that a truncated singular value decomposition, made up of a few of the largest singular values and associated right and left singular vectors, of the matrix of a large-scale linear discrete ill-posed problems can be computed quite inexpensively by an implicitly restarted Golub-Kahan bidiagonalization method. Similarly, for large symmetric discrete ill-posed problems a truncated eigendecomposition can be computed inexpensively by an implicitly restarted symmetric Lanczos method.