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.
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