An upper J-Hessenberg reduction of a matrix through symplectic Householder transformations. (1st July 2019)

• Record Type: Journal Article
• Authors: Salam, Ahmed; Kahla, Haithem Ben
• Is Part Of: Computers & mathematics with applications. Volume 78:issue 1(2019)
• Page Start: 178
• Page End: 190
• Publication Date: 2019-07-01
• Subjects: Indefinite inner product -- Structure-preserving eigenproblems -- Symplectic Householder transformations -- SR decomposition -- Upper J-Hessenberg form; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.02.025
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we introduce a reduction of a matrix to a condensed form, the upper J -Hessenberg form, via elementary symplectic Householder transformations, which are rank-one modification of the identity. Features of the reduction are highlighted and a general algorithm is derived. Then, we study different possibilities to specify the general algorithm in order to built better versions. We are led to two variants numerically more stables that we compare to JHESS algorithm. Also, some numerical experiments for comparing the different algorithms are given.