Mathematical Sciences: RUI: Numerical Solution of the Eigenvalue Problem of Symmetric Rationally Generated Toeplitz Matrices

本研究计划关注的是 的特征值和特征向量的计算 Toeplitz矩阵（其元素在第i行和第j列 仅取决于i-j）。 这样的矩阵自然出现在 微分方程的离散化以及从级数 解析函数的表示。 这其中的主要焦点 研究计划是为了降低计算成本， 特征值问题到一个点，它本质上是 与矩阵的大小无关。 Toeplitz矩阵的特征值问题出现在 所有应用领域。 这所追求的结果 研究计划将有利于所有科学领域， 工程.

This research program is concerned with the properties and computation of the eigenvalues and eigenvectors of Toeplitz matrices (whose element in the ith row and jth column depends only on i-j). Such matrices arise naturally in the discretization of differential equations as well as from series representation of analytic functions. The main focus of this research program is to reduce the computing cost for the eigenvalue problem to a point where it is essentially independent of the size of the matrix. Eigenvalue problems for Toeplitz matrices arise in all fields of applications. The results sought by this research program will benefit all areas of science and engineering.