Least-Squares on the Real Symplectic Group

Details Least-Squares on the Real Symplectic Group Least-Squares on the Real Symplectic Group

2010-01-06

arxiv.org/abs/1001.0829v1

Computer Science

Numerical Analysis

Scientific paper

The present paper discusses the problem of least-squares over the real symplectic group of matrices Sp(2n,R)$. The least-squares problem may be extended from flat spaces to curved spaces by the notion of geodesic distance. The resulting non-linear minimization problem on manifold may be tackled by means of a gradient-descent algorithm tailored to the geometry of the space at hand. In turn, gradient steepest descent on manifold may be implemented through a geodesic-based stepping method. As the space Sp(2n,R) is a non-compact Lie group, it is convenient to endow it with a pseudo-Riemannian geometry. Indeed, a pseudo-Riemannian metric allows the computation of geodesic arcs and geodesic distances in closed form on Sp(2n,R).

Affiliated with

Also associated with

No associations

Rating

Least-Squares on the Real Symplectic Group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Least-Squares on the Real Symplectic Group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Least-Squares on the Real Symplectic Group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-163937