Non-symbolic algorithms for the inversion of tridiagonal matrices

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:252

Article

Abderraman Marrero, J.¹  Rachidi, M.²  Tomeo, V.³ 

[1] Tech Univ Madrid, ETSIT UPM Telecommun Engn Sch, Dept Math Appl Informat Technol, Madrid 28040, Spain

[2] Univ Moulay Ismail, Fac Sci, Dept Math & Informat, Grp DEFA, Beni Mhamed, Meknes, Morocco

[3] Univ Complutense, EUE UCM Sch Stat, Dept Algebra, E-28040 Madrid, Spain

关键词: Computational complexity;    Difference equation;    Inverse matrix;    Numerical algorithm;    Tridiagonal matrix;   

DOI  :  10.1016/j.cam.2012.05.003

来源: Elsevier

【 摘 要 】

A representation for the entries of the inverse of general tridiagonal matrices is based on the determinants of their principal submatrices. It enables us to introduce, through the linear recurrence relations satisfied by such determinants, a simple algorithm for the entries of the inverse of any tridiagonal nonsingular matrix, reduced as well as unreduced. The numerical approach is preserved here, without invoking the symbolic computation. For tridiagonal diagonally dominant matrices, a scaling transformation on the recurrences allows us to give another algorithm to avoid overflow and underflow. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free