Improving formulas for the eigenvalues of finite block-Toeplitz tridiagonal matrices

J. Abderramán Marrero and D.A. Aiat Hadj

Applied Mathematics and Computation, 2020, vol. 382, issue C

Abstract: After a short overview, improvements (based on the Kronecker product) are proposed for the eigenvalues of (N × N) block-Toeplitz tridiagonal (block-TT) matrices with (K × K) matrix-entries, common in applications. Some extensions of the spectral properties of the Toeplitz-tridiagonal matrices are pointed-out. The eigenvalues of diagonalizable symmetric and skew-symmetric block-TT matrices are studied. Besides, if certain matrix square-root is well-defined, it is proved that every block-TT matrix with commuting matrix-entries is isospectral to a related symmetric block-TT one. Further insight about the eigenvalues of hierarchical Hermitian block-TT matrices, of use in the solution of PDEs, is also achieved.

Keywords: Block-matrix eigenvalues; Elliptical PDEs; Kronecker product; Matrix square-root; Polynomial matrix (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320302903

DOI: 10.1016/j.amc.2020.125324

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