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An isospectral transformation between Hessenberg matrix and Hessenberg-bidiagonal matrix pencil without using subtraction by Kobayashi, Katsuki; Maeda, Kazuki; Tsujimoto, Satoshi is a scholarly article available to read on EtoBox.

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We introduce an eigenvalue-preserving transformation algorithm from the generalized eigenvalue problem by matrix pencil of the upper and the lower bidiagonal matrices into a standard eigenvalue problem while preserving sparsity, using the theory of orthogonal polynomials. The procedure is formulated without subtraction, which causes numerical instability. Furthermore, the algorithm is discussed for the extended case where the upper bidiagonal matrix is of Hessenberg type.

Author

Kobayashi, Katsuki; Maeda, Kazuki; Tsujimoto, Satoshi

Published

2022

Language

EN