Adaptive filters for piecewise smooth spectral data

被引：31

作者：

Tadmor, E ^{[1
]}

Tanner, J

机构：

[1] Univ Maryland, Inst Phys Sci & Technol, Ctr Sci Computat & Math Modeling, Dept Math, College Pk, MD 20742 USA

[2] Stanford Univ, Dept Stat, Stanford, CA 94305 USA

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2005年 / 25卷 / 04期

基金：

美国国家科学基金会;

关键词：

Fourier series; filters; localization; piecewise smooth; spectral projection;

D O I：

10.1093/imanum/dri026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a new class of exponentially accurate filters for processing piecewise smooth spectral data. Our study is based on careful error decompositions, focusing on a rather precise balance between physical space localization and the usual moments condition. Exponential convergence is recovered by optimizing the order of the filter as an adaptive function of both the projection order and the distance to the nearest discontinuity. Combined with the automated edge detection methods, e.g. Gelb & Tadmor (2002, Math. Model. Numer. Anal., 36, 155-175)., adaptive filters provide a robust, computationally efficient, black box procedure for the exponentially accurate reconstruction of a piecewise smooth function from its spectral information.

引用

页码：635 / 647

页数：13