INTEGER POWERS OF ANTI-BIDIAGONAL HANKEL MATRICES

被引：1

作者：

da Silva, Joao Lita ^{[1
]}

机构：

[1] NOVA Univ Lisbon, Fac Sci & Technol, Dept Math & GeoBioTec, P-2829516 Quinta Da Torre, Caparica, Portugal

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2018年 / 49卷 / 01期

关键词：

Hankel matrices; anti-bidiagonal matrices; Chebyshev polynomials; TRIDIAGONAL MATRICES; LINEAR COMBINATION; ZEROS;

D O I：

10.1007/s13226-018-0256-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we derive a general expression for integer powers of real upper and lower anti-bidiagonal matrices with constant anti-diagonals using Chebyshev polynomials. An explicit formula for the inverse of these matrices is also provided.

引用

页码：87 / 98

页数：12

共 13 条

[1]

Chihara T.S., 1978, INTRO ORTHOGONAL POL

[2] Integer powers of anti-tridiagonal matrices of the form antitridiagn (a,c,-a), a, c ∈ C [J].

da Silva, Joao Lita .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2016, 93 (10) :1723-1740

[3] On anti-pentadiagonal persymmetric Hankel matrices with perturbed corners [J].

da Silva, Joao Lita .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 72 (03) :415-426

[4] Integer powers of anti-tridiagonal matrices of the form antitridiagn(a, 0, b), a, b ∈ R [J].

da Silva, Joao Lita .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 69 (11) :1313-1328

[5]

GOLUB H., 2013, Matrix Computations

[6] DETERMINATION OF THE ZEROS OF A LINEAR COMBINATION OF TSCHEBYSCHEV POLYNOMIALS [J].

GRANT, JA ;

GHIATIS, A .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1983, 3 (02) :193-206

[7] DETERMINATION OF THE ZEROS OF A LINEAR COMBINATION OF GENERALIZED POLYNOMIALS [J].

GRANT, JA ;

RAHMAN, AA .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1992, 42 (02) :269-278

[8] Powers of complex persymmetric or skew-persymmetric anti-tridiagonal matrices with constant anti-diagonals [J].

Gutierrez-Gutierrez, Jesus .

APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (13) :6125-6132

[9]

Mason JC., 2003, CHEBYSHEV POLYNOMIAL

[10]

Meyer Carl D., 2000, MATRIX ANAL APPL LIN, V71

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