The present paper discusses the problem of geodesic least squares over the real symplectic group of matrices Sp(2n,ℝ). As the space Sp(2n,ℝ) is a non-compact Lie group, it is convenient to endow it with a pseudo-Riemannian geometry instead of a Riemannian one. Indeed, a pseudo-Riemannian metric allows the computation of geodesic arcs and geodesic distances in closed form. ©2010 IEEE.
A pseudo-Riemannian-gradient approach to the least-squares problem on the real symplectic group / Fiori, Simone. - (2010), pp. 1954-1957. [10.1109/ICASSP.2010.5495296]
A pseudo-Riemannian-gradient approach to the least-squares problem on the real symplectic group
FIORI, Simone
2010-01-01
Abstract
The present paper discusses the problem of geodesic least squares over the real symplectic group of matrices Sp(2n,ℝ). As the space Sp(2n,ℝ) is a non-compact Lie group, it is convenient to endow it with a pseudo-Riemannian geometry instead of a Riemannian one. Indeed, a pseudo-Riemannian metric allows the computation of geodesic arcs and geodesic distances in closed form. ©2010 IEEE.File in questo prodotto:
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