Block Flexible GMRES variant with WY/Householder decomposition

A common problem in mathematics is the solving of linear systems. Finding an exact solution of a linear system is not affordable in most times; and not necessary, if we can choose a proper approximate. There are several families of methods to find such an approximate as techniques based on Krylov subspaces. All those techniques have in common, that they find a proper approximate in a Krylov subspace based on two main techniques we will present (FOM and GMRES), and enriched by a lot of variants of those two techniques (restarted, truncated, preconditioned etc.). All those variants appear in dual implementations, namely in a Gram-Schmidt and a Householder implementation. This is true as long as linear systems with a single right-hand side are considered. Considering multiple right-hand sides, the present literature only presents Block GMRES techniques using Gram-Schmidt orthogonalization ('Block' implies the multiple right-hand side). This book closes this gap in literature by presenting a Flexible Block GMRES technique for linear systems with multiple right-hand sides using the Householder orthogonalization or - as it is called for multiple right-hand sides -- the WY decomposition.

Autorentext

Joel Emanuel Fuchs, born in Scotland, moved to Wuppertal (Germany) in 1990. He studied Mathematics and wrote his bachelor thesis about algebraic geometry, following his master degree finalizing it with this examination of the GMRES algorithm. Additionally, he worked as data scientist and author at the University of Wuppertal.