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

本文研究了Toeplitz矩阵（其第i行第j列的元素仅依赖于i-j）的特征值和特征向量的性质及其计算。这种矩阵在微分方程的离散化以及解析函数的级数表示中自然出现。本研究计划的主要焦点是将特征值问题的计算成本降低到与矩阵大小无关的程度。Toeplitz矩阵的特征值问题在各个领域都有应用。这项研究计划所寻求的结果将有利于科学和工程的所有领域。

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.