Abstract
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.
| Original language | English |
|---|---|
| Number of pages | 19 |
| Volume | 1907:10550 |
| Publication status | Published - Jul 2019 |
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Keywords
- numerical analysis
- variable precision
- Krylov methods
- ilinear algebra
Cite this
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Exploiting variable precision in GMRES. / Gratton, Serge; Simon, Ehouarn; Titley-Peloquin, David; Toint, Philippe.
2019.Research output: Working paper
TY - UNPB
T1 - Exploiting variable precision in GMRES
AU - Gratton, Serge
AU - Simon, Ehouarn
AU - Titley-Peloquin, David
AU - Toint, Philippe
PY - 2019/7
Y1 - 2019/7
N2 - We describe how variable precision floating point arithmetic can be used inthe iterative solver GMRES. We show how the precision of the inner productscarried out in the algorithm can be reduced as the iterations proceed, withoutaffecting the convergence rate or final accuracy achieved by the iterates.Our analysis explicitly takes into account the resulting loss of orthogonalityin the Arnoldi vectors. We also show how inexact matrix-vector products canbe incorporated into this setting.
AB - We describe how variable precision floating point arithmetic can be used inthe iterative solver GMRES. We show how the precision of the inner productscarried out in the algorithm can be reduced as the iterations proceed, withoutaffecting the convergence rate or final accuracy achieved by the iterates.Our analysis explicitly takes into account the resulting loss of orthogonalityin the Arnoldi vectors. We also show how inexact matrix-vector products canbe incorporated into this setting.
KW - numerical analysis
KW - variable precision
KW - Krylov methods
KW - ilinear algebra
M3 - Working paper
VL - 1907:10550
BT - Exploiting variable precision in GMRES
ER -