Solution of large-scale weighted least-squares problems

Abstract

A sequence of least-squares problems of the form miny G1=2(ATy−h) 2, where G is an n×n positive definite diagonal weight matrix, and A an m×n (m6n) sparse matrix with some dense columns; has many applications in linear programming, electrical networks, elliptic boundary value problems, and structural analysis. We suggest low-rank correction preconditioners for such problems, and a mixed solver (a combination of a direct solver and an iterative solver). The numerical results show that our technique for selecting the low-rank correction matrix is very effective. Copyright ? 2002 John Wiley & Sons, Ltd.