Jens-Peter M. Zemke
Variants of IDR with partial orthonormalization

Type           : PREPRINT

MSC : 65F25 Orthogonalization 65F10 Iterative methods for linear systems, See also {65N22}
Language : ENGLISH

Format : application/pdf

Upload : 03/21/2016
We present four variants of IDR(s) that generate vectors such that consecutive blocks of s + 1 vectors are orthonormal. IDR methods are based on tuning parameters: an initially chosen, so-called shadow space, and the so-called seed values. We collect possible choices for the seed values. We prove that under certain conditions all four variants are mathematically equivalent and discuss possible breakdowns. We give an error analysis of all four variants and a numerical comparison in the context of the solution of linear systems and eigenvalue problems.

IDR; partial orthonormalization; minimum norm expansion; error analysis