A MAPPED POLYNOMIAL METHOD FOR HIGH-ACCURACY APPROXIMATIONS ON ARBITRARY GRIDS

被引：20

作者：

Adcock, Ben ^{[1
]}

Platte, Rodrigo B. ^{[2
]}

机构：

[1] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada

[2] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2016年 / 54卷 / 04期

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

equispaced nodes; scattered data; spectral methods; Runge phenomenon; analytic functions; FAST FOURIER-TRANSFORMS; QUADRATURE;

D O I：

10.1137/15M1023853

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The focus of this paper is the approximation of analytic functions on compact intervals from their pointwise values on arbitrary grids. We introduce a new method for this problem based on mapped polynomial approximation. By careful selection of the mapping parameter, we ensure both high accuracy of the approximation and an asymptotically optimal scaling of the polynomial degree with the grid spacing. As we explain, efficient implementation of this method can be achieved using nonuniform fast Fourier transforms. Numerical results demonstrate the efficiency and accuracy of this approach.

引用

页码：2256 / 2281

页数：26

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