Symplectic Householder transformations for a QR-like decomposition, a geometric and algebraic approaches

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摘要

The aim of this paper is to show how geometric and algebraic approaches lead us to a new symplectic elementary transformations: the 2-D symplectic Householder transformations. Their features are studied in details. Their interesting properties allow us to construct a new algorithm for computing a SR factorization. This algorithm is based only on these 2-D symplectic Householder transformations. Its new features are highlighted. The study shows that, in the symplectic case, the new algorithm is the corresponding one to the classical QR factorization algorithm, via the Householder transformations. Some numerical experiments are given.

论文关键词:65F15,65F50,Skew-symmetric inner product,Symplectic geometry,Symplectic transvections,Symplectic Householder transformations,Symplectic SR factorization

论文评审过程:Received 6 November 2006, Revised 4 March 2007, Available online 24 March 2007.

论文官网地址:https://doi.org/10.1016/j.cam.2007.03.015