Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2604.09883 |
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Inhaltsangabe:
- We study the direct and inverse spectral theory for a class of finite Hermitian banded matrices. Using the theory of matrix orthogonal polynomials, we provide an explicit procedure for reconstructing a banded matrix from a matrix-valued measure that encodes its spectral data. We establish necessary and sufficient conditions for a measure to be the spectral measure of a matrix in the examined class. We further analyze the connections between this spectral analysis, block tridiagonalization algorithms, and the Toda lattice evolution on banded matrices.