Multirate systems and filter banks
Multirate systems and filter banks
Splitting methods for SU(N) loop approximation
Journal of Approximation Theory
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In Oswald and Shingel (2009) [6], we proved an asymptotic O(n^-^@a^/^(^@a^+^1^)) bound for the approximation of SU(N) loops (N=2) with Lipschitz smoothness @a1/2 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 e^A^(^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 first-order splitting methods. In the present note we show that using higher order splitting methods allows us to improve the above suboptimal result to close-to-optimal O(n^-^(^@a^-^@e^)) bounds for @a1, where @e0 can be chosen arbitrarily small.