Symbolic algorithms for the inverses of general <i>k</i>-tridiagonal matrices

作     者：Jia, Jiteng Li, Sumei 

作者机构：Xidian Univ Sch Math & Stat Xian 710071 Shaanxi Peoples R China Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China 

出 版 物：《COMPUTERS & MATHEMATICS WITH APPLICATIONS》 (计算机与数学及其应用)

年 卷 期：2015年第70卷第12期

页      面：3032-3042页

核心收录：

学科分类：08[工学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Tridiagonal matrices k-tridiagonal matrices Inverses Block diagonalization Computational cost 

摘      要：Two symbolic algorithms for inverting k-tridiagonal matrices have been recently found by El-Mikkawy and Atlan (2014, 2015). These two algorithms are mainly based on the Doolittle LU factorization of the k-tridiagonal matrix. In the current paper, we present a new explicit analytic expression for the inverses of general tridiagonal matrices at first. By using a block diagonalization technique, we then relate k-tridiagonal matrix inversion to tridiagonal matrix inversion. Meanwhile, an efficient algorithm is derived for computing the inverses of nonsingular k-tridiagonal matrices with the help of any algorithm for computing the inverses of tridiagonal matrices. Three examples are given in order to illustrate the performance and efficiency of the proposed algorithms. (C) 2015 Elsevier Ltd. All rights reserved.