A PRECONDITIONER FOR THE LSQR ALGORITHM
Saeed Karimi, Davod Khojasteh Salkuyeh, F. Toutounian · Journal of applied mathematics & informatics · 2008
Iterative methods are often suitable for solving least squares problems minkAx bk2, where A 2 m◊n is large and sparse. The well known LSQR algorithm is among the iterative methods for solving these problems. A good preconditioner is often needed to speedup the LSQR con- vergence. In this paper we present the numerical experiments of applying a well known preconditioner for the LSQR algorithm. The preconditioner is based on the A T A-orthogonalization process which furnishes an incom- plete upper-lower factorization of the inverse of the normal matrix A T A. The main advantage of this preconditioner is that we apply only one of the factors as a right preconditioner for the LSQR algorithm applied to the least squares problem minkAx bk2. The preconditioner needs only the sparse matrix-vector product operations and significantly reduces the solution time compared to the unpreconditioned iteration. Finally, some numerical experiments on test matrices from Harwell-Boeing collection are presented to show the robustness and eciency of this preconditioner.