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

JOURNAL OF APPROXIMATION THEORY

卷:162

Article

Oswald, Peter¹  Shingel, Tatiana² 

[1] Jacobs Univ Bremen, D-28759 Bremen, Germany

[2] Univ Calif San Diego, La Jolla, CA 92093 USA

关键词: Nonlinearly constrained approximation;    Loop groups;    Jackson-type estimates;    Paraunitary FIR filters;    Splitting methods;   

DOI  :  10.1016/j.jat.2010.04.006

来源: Elsevier

【 摘 要 】

In Oswald and Shingel (2009) [6], we proved an asymptotic O(n(-alpha/(alpha+1))) bound for the approximation of SU(N) loops (N >= 2) with Lipschitz smoothness alpha > 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 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(-alpha/(alpha-epsilon))) bounds for alpha > I, where epsilon > 0 can be chosen arbitrarily small. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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