an:06756779
Zbl 1368.65066
Zemke, Jens-Peter M.
Variants of IDR with partial orthonormalization
EN
ETNA, Electron. Trans. Numer. Anal. 46, 245-272 (2017).
00363103
2017
j
65F25 65F10 65F15 65F50
IDR; partial orthonormalization; minimum norm expansion; error analysis
Summary: 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 \textit{shadow space}, and the so-called \textit{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.