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Preconditioning techniques for nonsymmetric and indefinite linear systems. (English) Zbl 0662.65028
This paper examines different techniques for solving large sparse linear systems which are nonsymmetric or indefinite by preconditioning techniques. Solving those systems by iterative schemes can be very hard and none of the examined techniques can be viewed as a general purpose solver. Alternatives considered for these cases are either to use direct methods or techniques based on the normal equations.
Examples show that the incomplete LQ factorization combined with the normal equation approach is one of the most promising methods. The author uses a Gram-Schmidt-process which is numerically stable because the rows remain very sparse in the incomplete LQ factorization. For the incompleteness of the factorization a dropping strategy is proposed which keeps only a fixes amount of largest elements in L and Q. The resulting algorithm is fairly economical and does not require allocating more space than necessary but it is not amenable to parallel or vector processing. As alternative methods the author describes the incomplete LU factorization with pivoting, SSOR and incomplete Cholesky on the normal equations.
Reviewer: N.K√∂ckler

65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
Full Text: DOI
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