Solution of large-scale weighted least-squares problems

A sequence of least squares problems of the form miny kG1=2(AT y h)k2, where G is an n n positive definite diagonal weight matrix, and A anm n (m n) 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 c 2000 John Wiley & Sons, Ltd.