SPARSE STRETCHING FOR SOLVING SPARSE-DENSE LINEAR LEAST-SQUARES PROBLEMS

• ID: 2822, RIV: 10405985
• ISSN: 1064-8275, ISBN: not specified
• source: SIAM Journal of Scientific Computing
• keywords: linear least-squares problems; dense rows; matrix stretching; sparse matrices
• authors: Jennifer A Scott, Miroslav Tůma
• authors from KNM: Tůma Miroslav

Abstract

Large-scale linear least-squares problems arise in a wide range of practical applications. In some cases, the system matrix contains a small number of dense rows. These make the problem significantly harder to solve because their presence limits the direct applicability of sparse matrix techniques. In particular, the normal matrix is (close to) dense, making a Cholesky factorization impractical. One way to help overcome the dense row problem is to employ matrix stretching. Stretching is a sparse matrix technique that improves sparsity by making the least-squares problem larger. We show that standard stretching can still result in the normal matrix for the stretched problem having an unacceptably large amount of fill. This motivates us to propose a new sparse stretching strategy that performs the stretching so as to limit the fill in the normal matrix and its Cholesky factor. Numerical examples from real problems are used to illustrate the potential gains.