Volume 46, pp. 245-272, 2017.
Variants of IDR with partial orthonormalization
Jens-Peter M. Zemke
Abstract
We present four variants of IDR that generate vectors such that
consecutive blocks of 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.
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Key words
IDR, partial orthonormalization, minimum norm expansion, error analysis
AMS subject classifications
65F25 (primary), 65F10, 65F15, 65F50
