14 citations · 46 across the 6 of their papers we have counts for
4 papers · 1 filter
Exploiting variable precision in GMRES
Serge Gratton, Ehouarn Simon, David Titley-Peloquin +1
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…
Minimizing convex quadratic with variable precision conjugate gradients
S. Gratton, E. Simon, D. Titley-Peloquin +1
We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance…
A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation
Serge Gratton, Selime Gürol, Ehouarn Simon +1
The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model a…
On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation
S. Gratton, S. Gürol, E. Simon +1
This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its orig…