Variants of IDR with partial orthonormalization

Jens-Peter M. Zemke

Abstract

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.

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Key words

IDR, partial orthonormalization, minimum norm expansion, error analysis

AMS subject classifications

65F25 (primary), 65F10, 65F15, 65F50

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