Parameter modified versions of preconditioning and iterative inner product free refinement methods for two-by-two block matrices
| Autor: | Zhao-Zheng Liang, Owe Axelsson |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory Preconditioner 010102 general mathematics MathematicsofComputing_NUMERICALANALYSIS Block matrix Chebyshev iteration 010103 numerical & computational mathematics Krylov subspace 01 natural sciences Chebyshev filter Mathematics::Numerical Analysis Rate of convergence Iterative refinement Discrete Mathematics and Combinatorics Applied mathematics Geometry and Topology 0101 mathematics Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Linear Algebra and its Applications. 582:403-429 |
| ISSN: | 0024-3795 |
| Popis: | A special two-by-two block matrix form arises in many important applications. Extending earlier results it is shown that parameter modified versions of a very efficient preconditioner does not improve its rate of convergence. This holds also for iterative refinement methods corresponding to a few fixed steps of the Chebyshev accelerated method. The parameter version can improve the defect-correction method but the convergence of this method is slower than an iterative refinement method with an optimal parameter. The paper includes also a discussion of how one can save computer elapsed times by avoiding use of global inner products such as by use of a Chebyshev accelerated method instead of a Krylov subspace method. Since accurate and even sharp eigenvalue bounds are available, the Chebyshev iteration method converges as fast as the Krylov subspace method. |
| Databáze: | OpenAIRE |
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