On new algorithms for inverting Hessenberg 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;    Hessenberg matrix;    Inverse matrix;    Matrix factorization;   

DOI  :  10.1016/j.cam.2012.11.003

来源: Elsevier

【 摘 要 】

A modification of the Ikebe algorithm for computing the lower half of the inverse of an (unreduced) upper Hessenberg matrix, extended to compute the entries of the superdiagonal, is considered in this paper. It enables us to compute the inverse of a quasiseparable Hessenberg matrix in O(n(2)) times. A new factorization expressing the inverse of a nonsingular Hessenberg matrix as a product of two suitable matrices is obtained. Because this allows us the use of back substitution for the inversion of triangular matrices, the inverse is computed with complexity O(n(3)). Some comparisons with results obtained using other recent inversion algorithms are also provided. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free