Wang, Kai; Zhang, Jun MSP: A class of parallel multistep successive sparse approximate inverse preconditioning strategies. (English) Zbl 1034.65022 SIAM J. Sci. Comput. 24, No. 4, 1141-1156 (2003). Summary: We develop a class of parallel multistep successive preconditioning (MSP) strategies to enhance efficiency and robustness of standard sparse approximate inverse preconditioning techniques. The key idea is to compute a series of simple sparse matrices to approximate the inverse of the original matrix. Studies are conducted to show the advantages of such an approach in terms of both improving preconditioning accuracy and reducing computational cost, compared to the standard sparse approximate inverse preconditioners. Numerical experiments using one prototype implementation to solve a few sparse matrices on a distributed memory parallel computer are reported. Cited in 8 Documents MSC: 65F10 Iterative numerical methods for linear systems 65F50 Computational methods for sparse matrices 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 65Y05 Parallel numerical computation Keywords:sparse matrices; preconditioning; sparse approximate inverse; parallel computation; multistage method; numerical experiments Software:ParaSails; BILUTM; BILUM; SparseMatrix PDFBibTeX XMLCite \textit{K. Wang} and \textit{J. Zhang}, SIAM J. Sci. Comput. 24, No. 4, 1141--1156 (2003; Zbl 1034.65022) Full Text: DOI