Performance comparison of preconditioned iterative methods with direct preconditioners (Q2925901)
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scientific article; zbMATH DE number 6362185
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Performance comparison of preconditioned iterative methods with direct preconditioners |
scientific article; zbMATH DE number 6362185 |
Statements
29 October 2014
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preconditioned AOR method
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\(L\)-matrix
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irreducible matrix
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triangular preconditioner
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Krylov subspace method
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accelerated overrelaxation
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preconditioning
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Performance comparison of preconditioned iterative methods with direct preconditioners (English)
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Consider the matrix \(A=I-L-U\), a decomposition of the matrix \(A\) into a diagonal, a lower- and an upper triangular part. To solve \(Ax=b\), the preconditioners \(P\) of the form \(P_l=I+\beta L\), \(P_u=I+\beta U\), or \(P_b=I+\beta(L+U)\) can be applied. Then the original and the preconditioned system can be solved by an AOR (accelerated overrelaxation) iterative method. Comparison theorems are given for the (spectral radius of the) iteration matrices of the AOR methods with and without preconditioning. A near optimal selection of the parameter \(\beta\) for the Krylov method is proposed for each of the preconditioners.
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