A new scheme of computing the approximate inverse preconditioner for the reduced linear systems

Authors:
K. Moriya;T. Nodera
Affiliations:
Department of Information and Integrated Technology, Aoyama Gakuin University, Japan;Department of Mathematics, Keio University, Japan
Venue:
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Year:
2007

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Abstract

In this paper, we propose a new implementation of the Newton scheme of an approximate preconditioner for the reduced linear system. In the original Newton scheme, the trouble is that the computation cost of the matrix-matrix product is always so expensive. On the other hand, the proposed implementation computes the preconditioner implicitly and reduces the cost of constructing the preconditioner by using the matrix-vector product form. We also show that the proposed implementation is less expensive than computing the preconditioner in explicit form.