An incomplete factorization method for preconditioning symmetric positive definite matrices is introduced to solve normal equations. The normal equations are formed as a means to solve rectangular matrices from linear least squares problems. The procedure is based on a block incomplete Cholesky factorization and a multilevel recursive strategy with an approximate Schur complement matrix formed implicitly. A diagonal perturbation strategy is implemented to enhance factorization robustness. The factors obtained are used as a preconditioner for the conjugate gradient method. Numerical experiments are used to show the robustness and efficiency of this preconditioning technique, and to compare it with two other preconditioners.
Technical Report No. 317-01, Department of Computer Science, University of Kentucky, Lexington, KY, 2001. This research was supported in part by the U.S. National Science Foundation under grants CCR-9902022, CCR-9988165 and CCR-0043861.