Local behaviors of Fourier expansions for functions of limited regularities

Based on the explicit formula of the pointwise error of Fourier projection approximation and by applying van der Corput-type Lemma, optimal convergence rates for periodic functions with different degrees of smoothness are established. It shows that the convergence rate enjoys a decay rate one order...

Full description

Saved in:

Bibliographic Details
Published in:	Advances in computational mathematics Vol. 50; no. 3
Main Authors:	Yang, Shunfeng, Xiang, Shuhuang
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-06-2024 Springer Nature B.V
Subjects:	Computational Mathematics and Numerical Analysis Computational Science and Engineering Convergence Decay rate Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Periodic functions Singularities Smoothness Visualization 65N15 42A20 42A10 Fourier expansion Convergence rate 41A60 Projection approximation Pointwise error Window function 42A16 Regularity
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	Based on the explicit formula of the pointwise error of Fourier projection approximation and by applying van der Corput-type Lemma, optimal convergence rates for periodic functions with different degrees of smoothness are established. It shows that the convergence rate enjoys a decay rate one order higher in the smooth parts than that at the singularities. In addition, it also depends on the distance from the singularities. Ample numerical experiments illustrate the perfect coincidence with the estimates.
ISSN:	1019-7168 1572-9044
DOI:	10.1007/s10444-024-10136-5