Nonstationary multisplittings with general weighting matrices (Q2706308)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonstationary multisplittings with general weighting matrices |
scientific article |
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19 March 2001
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linear systems
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iterative methods
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parallel algorithms
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symmetric positive definite and semidefinite matrices
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weighted splitting
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convergence
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Nonstationary multisplittings with general weighting matrices (English)
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During an iterative solution of a system of linear algebraic equations with a symmetric positive definite matrix \(A\), one may split the matrix \(A = M - N\) repeatedly, i.e., using some \(p\) different splittings with non-singular \(M\)'s and with related scalar weights \(E\). A parallelized version of such an algorithm requires a matrix form of \(E\). The paper offers the corresponding generalization of the convergence theorems. Thus, one can make several iterations (with a ``non-stationary'' block-dependence of their number) in each processor. The authors also extend their analysis to two-stage parallelized iterative treatment of a semi-definite matrix \(A\).
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