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Journal of Function Spaces
Volume 2016, Article ID 5780718, 7 pages
http://dx.doi.org/10.1155/2016/5780718
Research Article

Fast Analytic Sampling Approximation from Cauchy Kernel

1College of Mathematics and Information Science, Guangxi University, China
2Department of Mathematics, Shantou University, China

Received 4 November 2015; Accepted 22 February 2016

Academic Editor: Kehe Zhu

Copyright © 2016 Youfa Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper aims at establishing a fast numerical algorithm for , where is any function in the Hardy space and is the scale level. Here, is an approximation to we recently constructed by applying the multiscale transform to the Cauchy kernel. We establish the matrix expression of and find that it has the structure of a multilevel Hankel matrix. Based on the structure, a fast numerical algorithm is established to compute . The computational complexity is given. A numerical experiment is carried out to check the efficiency of our algorithm.