Some results on determinants and inverses of nonsingular pentadiagonal matrices

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:275

Article

Abderraman Marrero, J.¹  Tomeo, V.² 

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

[2] Univ Complutense, Fac Stat Studies, Dept Algebra, E-28040 Madrid, Spain

关键词: Computational complexity;    Determinant;    Inverse matrix;    Pentadiagonal matrix;    Structured matrix;   

DOI  :  10.1016/j.cam.2014.03.016

来源: Elsevier

【 摘 要 】

A block matrix analysis is proposed to justify, and modify, a known algorithm for computing in O(n) time the determinant of a nonsingular n x n pentadiagonal matrix (n >= 6) having nonzero entries on its second subdiagonal. Also, we describe a procedure for computing the inverse matrix with acceptable accuracy in O(n(2)) time. In the general nonsingular case, for n >= 5, proper decompositions of the pentadiagonal matrix, as a product of two structured matrices, allow us to obtain both the determinant and the inverse matrix by exploiting low rank structures. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free