Two algorithms for solving a general backward tridiagonal linear systems A.A. Karawia Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt Abstract In this paper we present an efficient computational and symbolic algorithms for solving a backward tridiagonal linear systems. The implementation of the algorithm using Computer algebra systems (CAS) such as Maple, Macsyma, Math- ematica, and Matlab is straightforward. An examples are given in order to illustrate the algorithms. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Backward tridiagonal matrices; Tridiagonal matrices; Linear systems; Determinants; Computer algebra systems (CAS) 1. Introduction Many problems in mathematics and applied science require the solution of linear systems having a backward tridiagonal coefficient matrices. This kind of linear system arise in many fields of numerical computation [1,2]. The main goal of the current paper is to develop an efficient algorithms for solving a general backward tridiagonal linear systems of the form: AX ¼ Y ; ð1:1Þ where A ¼ 0 0 0  0 a 1 d 1 0 0 0  a 2 d 2 b 2 0 0 0  d 3 b 3 0 . . . . . .     . . . . . . . . .     . . . a n1 d n1 b n1  0 0 0 d n b n 0  0 0 0 2 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 5 ; ð1:2Þ X ¼ðx 1 ; x 2 ; ... ; x n Þ T , Y ¼ðy 1 ; y 2 ; ... ; y n Þ T and n P 3. 0096-3003/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2007.04.057 E-mail address: abibka@mans.edu.eg Available online at www.sciencedirect.com Applied Mathematics and Computation 194 (2007) 534–539 www.elsevier.com/locate/amc