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Simultaneous similarity reductions for a pair of matrices to condensed forms. (English) Zbl 1312.65071

The authors present algorithms that simultaneously reduce a pair of square matrices to upper Hessenberg and lower Hessenberg forms through a similarity transformation, by considering special matrix pairs, then they recover the standard Arnoldi algorithm as well as the non-symmetric Lanczos algorithm. A numerical example on a model problem is presented to demonstrate this useful approximation property.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A21 Canonical forms, reductions, classification

Software:

ABLE; SparseMatrix
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Full Text: DOI

References:

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