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On the monotonicity of incomplete factorization. (English) Zbl 0682.65015

The Meijerink, van der Vorst type incomplete decomposition uses a position set, where the factors must be zero, but their product may differ from the original matrix. The smaller this position set is, the more the product of incomplete factors resembles the original matrix. The aim of this paper is to discuss this type of monotonicity. It is shown using the Perron Frobenius theory of nonnegative matrices, that the spectral radius of the iteration matrix is a monotone function of the position set. On the other hand no matrix norm of the iteration matrix depends monotonically on the position set. Comparison is made with the modified incomplete factorization technique.
Reviewer: T.Fiala

MSC:

65F10 Iterative numerical methods for linear systems
15A18 Eigenvalues, singular values, and eigenvectors
15B48 Positive matrices and their generalizations; cones of matrices
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References:

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