Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces
Volume 2017, Article ID 9376505, 7 pages
Research Article

Approximation of Functions on a Square by Interpolation Polynomials at Vertices and Few Fourier Coefficients

1College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China
2Joint Centre for Global Change Studies, Beijing, China

Correspondence should be addressed to Zhihua Zhang; nc.ude.unb@hzgnahz

Received 9 December 2016; Accepted 19 March 2017; Published 22 May 2017

Academic Editor: Hua Su

Copyright © 2017 Zhihua Zhang. 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.


For a bivariate function on a square, in general, its Fourier coefficients decay slowly, so one cannot reconstruct it by few Fourier coefficients. In this paper we will develop a new approximation scheme to overcome the weakness of Fourier approximation. In detail, we will use Lagrange interpolation and linear interpolation on the boundary of the square to derive a new approximation scheme such that we can use the values of the target function at vertices of the square and few Fourier coefficients to reconstruct the target function with very small error.