On inverses of tridiagonal matrices

被引：1

作者：

Al-Hassan, Qassem M. ^{[1
]}

机构：

[1] Univ Sharjah, Dept Basic Sci, Sharjah, U Arab Emirates

来源：

JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY | 2005年 / 8卷 / 01期

关键词：

Tridiagonal matrices; Crout's LU factorization; recurrence relation;

D O I：

10.1080/09720529.2005.10698020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An algorithm for computing the inverse of a general tridiagonal matrix is introduced. This algorithm is obtained by factoring this matrix into the product of two bidiagonal matrices using Crout's LU factorization, one upper and one lower bidiagonal. A simple recurrence relation is used to generate a sequence of numbers, this sequence is then used to fill in the matrices L, u, L-1, u(-1) and consequently the required inverse.

引用

页码：49 / 58

页数：10

共 50 条

[31] THE INVERSE EIGENVECTOR PROBLEM FOR REAL TRIDIAGONAL MATRICES
Parlett, Beresford
Dopico, Froilan M.
Ferreira, Carla
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2016, 37 (02) : 577 - 597
[32] ANALYTIC RESULTS FOR THE EIGENVALUES OF CERTAIN TRIDIAGONAL MATRICES
Willms, Allan R.
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2008, 30 (02) : 639 - 656
[33] Positive integer powers of certain tridiagonal matrices
Gutierrez-Gutierrez, Jesus
APPLIED MATHEMATICS AND COMPUTATION, 2008, 202 (01) : 133 - 140
[34] A RECURSIVE PARTITIONING ALGORITHM FOR INVERTING TRIDIAGONAL MATRICES
CHAWLA, MM
PASSI, K
SHIVAKUMAR, PN
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1990, 35 (1-4) : 153 - 158
[35] On some quasi anti-tridiagonal matrices
da Fonseca, Carlos M.
JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, 2021, 24 (04) : 1043 - 1052
[36] On the infinitesimal limits of the Schur complements of tridiagonal matrices
Somasunderam, Naveen
Chandrasekaran, Shivkumar
LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (03) : 659 - 681
[37] A simplified pivoting strategy for symmetric tridiagonal matrices
Bunch, James R.
Marcia, Roummel F.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2006, 13 (10) : 865 - 867
[38] THE PROBLEM OF GLOBAL IDENTIFIABILITY FOR SYSTEMS WITH TRIDIAGONAL MATRICES
Canto, Begona
Coll, Carmen
Sanchez, Elena
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 31 : 250 - 257
[39] A RECURSIVE DOUBLING-ALGORITHM FOR INVERTING TRIDIAGONAL MATRICES
CHAWLA, MM
PASSI, K
ZALIK, RA
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1990, 37 (3-4) : 213 - 220
[40] Some new improvements for bounds on the inverse of tridiagonal matrices
Jiang, Jianxin
Li, Yanyan
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE OF MATRICES AND OPERATORS (MAO 2012), 2012, : 4 - 7

← 1 2 3 4 5 →