Reliable updated residuals in hybrid Bi-CG methods
| Autor: | H.A. van der Vorst, Gerard L. G. Sleijpen |
|---|---|
| Rok vydání: | 1996 |
| Předmět: |
Numerical Analysis
Mathematical optimization Iterative method Linear system Residual Computer Science Applications Theoretical Computer Science Computational Mathematics Computational Theory and Mathematics Biconjugate gradient stabilized method Conjugate gradient method Convergence (routing) Algorithm Computer communication networks Software Mathematics |
| Zdroj: | Computing. 56:141-163 |
| ISSN: | 1436-5057 0010-485X |
| DOI: | 10.1007/bf02309342 |
| Popis: | Many iterative methods for solving linear equationsAx=b aim for accurate approximations tox, and they do so by updating residuals iteratively. In finite precision arithmetic, these computed residuals may be inaccurate, that is, they may differ significantly from the (true) residuals that correspond to the computed approximations. In this paper we will propose variants on Neumaier's strategy, originally proposed for CGS, and explain its success. In particular, we will propose a more restrictive strategy for accumulating groups of updates for updating the residual and the approximation, and we will show that this may improve the accuracy significantly, while maintaining speed of convergence. This approach avoids restarts and allows for more reliable stopping criteria. We will discuss updating conditions and strategies that are efficient, lead to accurate residuals, and are easy to implement. For CGS and Bi-CG these strategies are particularly attractive, but they may also be used to improve Bi-CGSTAB, BiCGstab(l), as well as other methods. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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