Research on the algebraic structure of theToda type non-autonomous discrete integrable systems and its applications

利用正交多项式理论和Hirota的tau函数理论，对Toda方程及其相关的离散可积系统进行了分析。我们特别关注“非自治离散可积系统”。然后，我们可以从特殊函数的角度来构建这些系统的理论。此外，我们给出了一类广义特征值问题的数值算法。

The analysis on the Toda equation and its related discrete integrable systems has been developed by using the theory of the orthogonal polynomials and the theory of Hirota's tau-function. In particular, we focus on the "non-autonomous discrete integrable systems". Then we are able to construct the theory of these systems from the point of view of the special functions. In addition, we formulate the numerical algorithms of some class of the generalized eigenvalue problems.