December, 2022. arXiv:2212.11577 [nlin]

Paper doi abstract bibtex

Paper doi abstract bibtex

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.

@misc{kobayashi_isospectral_2022, title = {An isospectral transformation between {Hessenberg} matrix and {Hessenberg}-bidiagonal matrix pencil without using subtraction}, url = {http://arxiv.org/abs/2212.11577}, doi = {10.48550/arXiv.2212.11577}, abstract = {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.}, urldate = {2023-01-08}, publisher = {arXiv}, author = {Kobayashi, Katsuki and Maeda, Kazuki and Tsujimoto, Satoshi}, month = dec, year = {2022}, note = {arXiv:2212.11577 [nlin]}, keywords = {linear algebra, mentions sympy, numerical analysis, spectral theory}, }

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