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Variants of IDR with partial orthonormalization. (English) Zbl 1368.65066
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 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.
##### MSC:
 65F25 Orthogonalization in numerical linear algebra 65F10 Iterative numerical methods for linear systems 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 65F50 Computational methods for sparse matrices
##### Software:
Algorithm 913; BiCGstab; mctoolbox
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