An implicit wavelet sparse approximate inverse preconditioner using block finger pattern
Akira Imakura, Tomohiro Sogabe, Shao Liang Zhang · Numerical Linear Algebra with Applications · 2009
Abstract Recently, an implicit wavelet sparse approximate inverse (IW‐SPAI hereafter) preconditioner has been proposed by Hawkins and Chen for nonsymmetric linear systems. The preconditioning matrix of the IW‐SPAI is characterized by a special sparse structure, the so‐calledfinger pattern, which makes it possible to construct a good sparse approximate inverse. Since the IW‐SPAI requires a number of QR factorizations with substantial costs to construct the preconditioner, there is a strong need to construct the IW‐SPAI more efficiently. The target of this paper is to reduce the costs of the IW‐SPAI using Haar basis. Under the strategy of classifying the QR factorizations into several groups and reducing the number of QR factorizations, in this paper, we introduce ablock finger patternfor Haar basis in the place of the finger pattern as the nonzero pattern of the preconditioning matrix. From the block finger pattern, we propose an implicit wavelet sparse approximate inverse preconditioner using block finger pattern (BIW‐SPAI hereafter). Numerical experiments indicate that the BIW‐SPAI is often more efficient than the IW‐SPAI. Copyright © 2009 John Wiley & Sons, Ltd.