The study of Jacobi and cyclic Jacobi matrix eigenvalue problems using Sturm-Liouville theory

被引：9

作者：

Kong, Qingkai ^{[1
]}

Zettl, Anton ^{[1
]}

机构：

[1] No Illinois Univ, Dept Math, De Kalb, IL 60115 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 434卷 / 07期

关键词：

Matrix eigenvalue problems; Jacobi and cyclic Jacobi matrices; Sturm-Liouville theory;

D O I：

10.1016/j.laa.2010.04.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the eigenvalues of matrix problems involving Jacobi and cyclic Jacobi matrices as functions of certain entries. Of particular interest are the limits of the eigenvalues as these entries approach infinity. Our approach is to use the recently discovered equivalence between these problems and a class of Sturm-Liouville problems and then to apply the Sturm-Liouville theory. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1648 / 1655

页数：8

共 7 条

[1]

Atkinson FV., 1964, Discrete and Continuous Boundary Value Problems

[2]

GANTMACHER FR, 2002, OSCILLATION MATRICES

[3]

Horn R.A., 2012, Matrix Analysis

[4] Sturm-Liouville problems on time scales with separated boundary conditions [J].