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Exploiting variable precision in GMRES

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arxiv 1907.10550 v2 pith:JETLATKF submitted 2019-07-24 math.NA cs.NA

Serge Gratton , Ehouarn Simon , David Titley-Peloquin , Philippe Toint This is my paper · ORCID
classification math.NAcs.NA
keywords precisiongmresproductsvariableaccountaccuracyachievedaffecting
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We describe how variable precision floating point arithmetic can be used 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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  1. Parameter optimization for restarted mixed precision iterative sparse solver

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    A k-nearest-neighbors classifier using the sparsity graph pseudo-diameter selects the single-to-double precision switching point in mixed-precision CG and achieves near-oracle efficiency on synthetic matrices.

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