An upper $J$- Hessenberg reduction of a matrix through symplectic Householder transformations
arXiv:1612.087074 citationsh-index: 5
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Provides a new matrix reduction technique for symplectic linear algebra, but the practical impact is limited to specialized numerical methods.
The paper introduces a reduction of a matrix to upper J-Hessenberg form using symplectic Householder transformations, and presents two numerically stable variants with experimental evidence of efficiency.
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. Two variants numerically more stables are then derived. Some numerical experiments are given, showing the efficiency of these variants.