Approximation of Functions on a Square by Interpolation Polynomials at Vertices and Few Fourier Coefficients. (22nd May 2017)

• Record Type: Journal Article
• Authors: Zhang, Zhihua
• Other Names: Su Hua Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2017(2017)
• Publication Date: 2017-05-22
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2017/9376505
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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.