Convergence of multisplitting methods with different weighting schemes (Q2890573)
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scientific article; zbMATH DE number 6044955
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence of multisplitting methods with different weighting schemes |
scientific article; zbMATH DE number 6044955 |
Statements
11 June 2012
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weighting schemes
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multisplitting method
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\(H\)-matrix
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convergence
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accelerated overrelaxation (AOR)
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symmetric successive overrelaxation (SSOR)
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Convergence of multisplitting methods with different weighting schemes (English)
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The paper deals with two multisplitting methods for solving a linear system whose coefficient matrix is an \(H\)-matrix. The accelerated overrelaxation (AOR)-like and symmetric successive overrelaxation (SSOR)-like multisplitting variants with a weighting are studied. The main convergence result for each of these variants proves that the spectral radiuses of the respective iterative matrices are less than \(1\) for each value of the weighting parameter from the interval \([0,1]\). The main part of the paper is devoted to technical proofs of the theorems. The numerical experiments are postponed to a future work. Reviewer's remark: The paper is rather theoretical than practical and the opinion of the referee is that the studied techniques are overcome in the present time.
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