Monotone convergence of iterative methods for singular linear systems (Q1864780)
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scientific article; zbMATH DE number 1886393
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Monotone convergence of iterative methods for singular linear systems |
scientific article; zbMATH DE number 1886393 |
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Monotone convergence of iterative methods for singular linear systems (English)
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11 January 2004
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Monotonicity of iterative methods for singular systems is discussed. Results of \textit{A. Berman} and \textit{R. J. Plemmons} [Nonnegative matrices in the mathematical sciences (1979; Zbl 0484.15016)], and \textit{P. Semal} [Linear Algebra Appl. 230, 35-46 (1995; Zbl 0844.65107)] are generalized to the case of singular systems. It is shown that for a nonnegative splitting of the coefficient matrix there exist initial guesses such that the iterative sequence converges towards a solution of the system. The monotonicity of the block Gauss-Seidel method for solving a \(p\)-cyclic system and Markov chains is considered.
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singular linear systems
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iterative methods
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semi-convergence
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monotonicity
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nonnegative splitting
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block Gauss-Seidel method
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\(p\)-cyclic system
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Markov chains
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