Displaying 261 – 280 of 549

Showing per page

Mixed precision GMRES-based iterative refinement with recycling

Oktay, Eda, Carson, Erin (2023)

Programs and Algorithms of Numerical Mathematics

With the emergence of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes for solving linear systems A x = b have recently been developed. However, in certain settings, GMRES may require too many iterations per refinement step, making it potentially more expensive than the alternative of recomputing the LU factors in a higher precision. In this work, we incorporate the idea of Krylov subspace recycling, a well-known technique for reusing information across sequential invocations,...

Model analysis of BPX preconditioner based on smoothed aggregation

Pavla Fraňková, Jan Mandel, Petr Vaněk (2015)

Applications of Mathematics

We prove nearly uniform convergence bounds for the BPX preconditioner based on smoothed aggregation under the assumption that the mesh is regular. The analysis is based on the fact that under the assumption of regular geometry, the coarse-space basis functions form a system of macroelements. This property tends to be satisfied by the smoothed aggregation bases formed for unstructured meshes.

Currently displaying 261 – 280 of 549