Using successive approximations for improving the convergence of GMRES method (Q1979007)
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scientific article; zbMATH DE number 1450157
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Using successive approximations for improving the convergence of GMRES method |
scientific article; zbMATH DE number 1450157 |
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Using successive approximations for improving the convergence of GMRES method (English)
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22 May 2000
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A possibility how to improve the convergence of the GMRES method for the iterative solution of the system \((I-T)x=b\) of linear algebraic equations with a nonsymmetric matrix is suggested. It consists in performing \(m\) pre-iterations of the form \(y_{l+1}=Ty_l+b\) before starting GMRES and in putting \(y_m\) as the initial approximation for GMRES. From the practical point of view, such pre-processing seems to be advantageous since one iteration of the pre-processing process costs less work that one of GMRES. Numerical tests confirm this hypothesis and the theory presented in the paper explains this observations.
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GMRES
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iterative method
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numerical experiments
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solution of dicsretized equations
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