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Exploiting variable precision in GMRES

Abstract : We describe how variable precision floating-point arithmetic can be used to compute inner products in the iterative solver GMRES. We show how the precision of the inner products carried out in the algorithm can be reduced as the iterations proceed, without affecting the convergence rate or final accuracy achieved by the iterates. Our analysis explicitly takes into account the resulting loss of orthogonality in the Arnoldi vectors. We also show how inexact matrix-vector products can be incorporated into this setting.
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https://hal.archives-ouvertes.fr/hal-02943241
Contributor : Serge Gratton <>
Submitted on : Friday, September 18, 2020 - 5:53:21 PM
Last modification on : Wednesday, October 14, 2020 - 4:17:13 AM

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1907.10550.pdf
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  • HAL Id : hal-02943241, version 1

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Serge Gratton, Ehouarn Simon, David Titley-Peloquin, Philippe Toint. Exploiting variable precision in GMRES. 2020. ⟨hal-02943241⟩

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