Splitting Methods for SU(N) Loop Approximation

Details Splitting Methods for SU(N) Loop Approximation Splitting Methods for SU(N) Loop Approximation

2006-12-21

arxiv.org/abs/math/0612645v2

Mathematics

Numerical Analysis

14 pages, still submitted to J. Approx. Th. typos corrected, part of the proof of Lemma 4 concerning the auxiliary statement o

Scientific paper

The problem of finding the correct asymptotic rate of approximation by polynomial loops in dependence of the smoothness of the elements of a loop group seems not well-understood in general. For matrix Lie groups such as SU(N), it can be viewed as a problem of nonlinearly constrained trigonometric approximation. Motivated by applications to optical FIR filter design and control, we present some initial results for the case of SU(N)-loops, N>1. In particular, using representations via the exponential map and ideas from splitting methods, we prove that the best approximation of an SU(N)-loop belonging to a Hoelder-Zygmund class Lip_alpha with alpha>1/2 by a polynomial SU(N)-loop of degree n is of the order O(n^{-\alpha/(1+\alpha)}) as n tends to infinity. Although this approximation rate is not considered final (and can be improved in special cases), to our knowledge it is the first general, nontrivial result of this type.

Affiliated with

Also associated with

No associations

Rating

Splitting Methods for SU(N) Loop Approximation 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 Splitting Methods for SU(N) Loop Approximation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Splitting Methods for SU(N) Loop Approximation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-22580