Close-to-optimal bounds for SU(N) loop approximation

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Close-to-optimal bounds for SU(N) loop approximation
In [6], we proved an asymptotic O(n−α/(α+1)) bound for the approximation of SU(N) loops (N ≥ 2) with Lipschitz smoothness α > 1/2 by polynomial loops of degree ≤ n. The proof combined factorizations of SU(N) loops into products of constant SU(N) matrices and loops of the form eA(t) where A(t) are essentially su(2) loops preserving the Lipschitz smoothness, and the careful estimation of errors induced by approximating matrix exponentials by firstorder splitting methods. In the present note we show that using higher order splitting methods allows us to improve the initial estimates from [6] to closeto-optimal O(n−(α− )) bounds for α > 1, where > 0 can be chosen arbitrarily small.
Peter Oswald, Tatiana Shingel
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JAT
Authors Peter Oswald, Tatiana Shingel
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