带状厄米矩阵、矩阵正交多项式与Toda格
Banded Hermitian Matrices, Matrix Orthogonal Polynomials, and the Toda Lattice
AI总结：
研究有限带状厄米矩阵的谱理论，利用矩阵正交多项式从矩阵值测度重构矩阵，并建立测度为谱测度的充要条件，同时分析其与块三对角化算法及Toda格演化的联系。
摘要：
我们研究一类有限厄米带状矩阵的直接和逆谱理论。利用矩阵正交多项式理论，我们提供了一个从编码其谱数据的矩阵值测度重构带状矩阵的显式程序。我们建立了测度为所研究类中矩阵的谱测度的必要和充分条件。我们进一步分析了该谱分析、块三对角化算法以及带状矩阵上的Toda格演化之间的联系。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
