On computing the determinants and inverses of some special type of tridiagonal and constant-diagonals matrices

被引：22
作者：
Witula, Roman [1 ]
Slota, Damian [1 ]
机构：
[1] Silesian Tech Univ, Inst Math, PL-44100 Gliwice, Poland
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2007年 / 189卷 / 01期
关键词：
tridiagonal matrices; Chebyshev polynomials; Fibonacci; Lucas numbers;
D O I：
10.1016/j.amc.2006.11.112
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The determinants and inverses of some tridiagonal and constant-diagonals matrices are discussed in the paper. Linear recurrence equations of the second and higher orders which satisfy these determinants are presented here. In connection with these determinants new families of polynomials are defined. The relationships between these polynomials and normed Chebyshev polynomials of the first and second kind are investigated. Incidentally, a number of new identities for Chebyshev polynomials and some linear modifications of these polynomials are shown, as well as many new trigonometric identities and identities for Fibonacci and Lucas numbers. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：514 / 527
页数：14
相关论文
共 17 条
  • [1] [Anonymous], 2001, FIBONACCI LUCAS NUMB, DOI DOI 10.1002/9781118033067
  • [2] Cahill ND, 2004, FIBONACCI QUART, V42, P216
  • [3] Cahill ND, 2003, FIBONACCI QUART, V41, P13
  • [4] A note on a three-term recurrence for a tridiagonal matrix
    El-Mikkawy, M
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2003, 139 (2-3) : 503 - 511
  • [5] Faddeev DK., 1965, PROBLEMS HIGHER ALGE
  • [6] Grzymkowski R., 2000, CALCULUS METHODS ALG
  • [7] Herceg D, 2001, FIBONACCI QUART, V39, P27
  • [8] Il'in V. P., 1985, TRIDIAGONAL MATRICES
  • [9] PAZKOWSKI S, 1975, NUMERICAL APPL CHEBY
  • [10] POLYA G, 1998, PROBLEMS THEOREMS AN, V1
12