A multilevel block incomplete Cholesky preconditioner for solving normal equations in linear least squares problems

Authors:
Jun Zhang;Tong Xiao
Affiliations:
Laboratory for High Performance Scientific Computing and Computer Simulation, Department of Computer, University of Kentucky, 773 Anderson Hall, Lexington, KY;Laboratory for High Performance Scientific Computing and Computer Simulation, Department of Computer, University of Kentucky, 773 Anderson Hall, Lexington, KY
Venue:
The Korean Journal of Computational & Applied Mathematics
Year:
2003

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Abstract

An incomplete factorization method for preconditioning symmetric positive definite matrices is introduced to solve normal equations. The normal equations are form to solve 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.