Powers of tridiagonal matrices with constant diagonals

被引：15

作者：

Gutierrez-Gutierrez, Jesus ^{[1
,2
]}

机构：

[1] CEIT, E-20018 San Sebastian, Spain

[2] Tecnun Univ Navarra, E-20018 San Sebastian, Spain

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2008年 / 206卷 / 02期

关键词：

Tridiagonal matrices; Eigenvalues; Eigenvectors; Jordan's form; Chebyshev polynomials;

D O I：

10.1016/j.amc.2008.10.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we derive a general expression for the entries of the qth power (q is an element of N) of the n x n complex tridiagonal matrix tridiag(n) (a(1); a(0); a(-1)) for all n is an element of N, in terms of the Chebyshev polynomials of the second kind. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：885 / 891

页数：7

共 7 条

[1] Positive integer powers of certain tridiagonal matrices
Gutierrez-Gutierrez, Jesus
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 202 (01) : 133 - 140
[2] On computing of arbitrary positive integer powers for one type of even order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis - I
Rimas, J
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 174 (02) : 997 - 1000
[3] On computing of arbitrary positive integer powers for one type of odd order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis-II
Rimas, Jonas
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 186 (01) : 872 - 878
[4] On computing of arbitrary positive integer powers for one type of odd order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis - I
Rimas, Jonas
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 183 (02) : 1378 - 1380
[5] On computing of arbitrary positive integer powers for one type of even order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis-II
Rimas, Jonas
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 181 (02) : 1120 - 1125
[6] ON THE EIGENVALUE PROBLEM FOR TOEPLITZ BAND MATRICES
TRENCH, WF
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1985, 64 (JAN) : 199 - 214
[7] Some phenomenon of the powers of certain tridiagonal and asymmetric matrices
Witula, Roman
Slota, Damian
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 202 (01) : 348 - 359

← 1 →