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

Author

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  • Abderramán Marrero, J.
  • Aiat Hadj, D.A.

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.

Suggested Citation

  • Abderramán Marrero, J. & Aiat Hadj, D.A., 2020. "Improving formulas for the eigenvalues of finite block-Toeplitz tridiagonal matrices," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    • Handle: RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320302903
    DOI: 10.1016/j.amc.2020.125324
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