Rectangular Sparse Matrices from Linear Least Squares Problems

Laboratory for High Performance Scientific Computing and Computer Simulation

Department of Computer Science

University of Kentucky

773 Anderson Hall

Lexington, KY 40506-0046, USA

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.

Key words: incomplete Cholesky factorization, multilevel IC preconditioner, normal equation, conjugate gradient.

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This paper has been accepted for publication in

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.