On Preconditioning Schur Complemenmt
and Schur Complement Preconditioning

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA


We study two implementation strategies to utilize Schur complement technique in multilevel recursive incomplete LU preconditioning techniques (RILUM) for solving general sparse matrices. The first strategy constructs a RILUM to precondition the original matrix. The second strategy solves the first Schur complement matrix using the lower level parts of the RILUM as the preconditioner. We discuss computational and memory costs of both strategies and the potential effect on grid independent convergence rate of RILUM with different implementation strategies.

Key words: Sparse matrices, Schur complement, RILUM, preconditioning techniques

This paper has been published in Electronic Transactions in Numerical Analysis, Vol. 10, 115-130, 2000. Technical Report 287-99, Department of Computer Science, University of Kentucky, Lexington, KY, 1999. The author's research work was supported in part by US National Science Foundation under grant CCR-9902022 and in part by the University of Kentucky Center for Computational Sciences.