A windowed fourier method for approximation of non-periodic functions on equispaced nodes

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

A windowed Fourier method is proposed for approximation of nonperiodic functions on equispaced nodes. Spectral convergence is obtained in most of the domain, except near the boundaries, where polynomial least-squares is used to correct the approximation. Because the method can be implemented using partition of unit and domain decomposition, it is suitable for adaptive and parallel implementations and large scale computations. Computations can be carried out using fast Fourier transforms. Comparisons with Fourier extension, rational interpolation and least-squares methods are presented.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computational Science and Engineering
PublisherSpringer Verlag
Pages405-413
Number of pages9
Volume106
ISBN (Print)9783319197999
DOIs
StatePublished - 2015
Event10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014 - Salt Lake City, United States
Duration: Jun 23 2014Jun 27 2014

Publication series

NameLecture Notes in Computational Science and Engineering
Volume106
ISSN (Print)14397358

Other

Other10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014
CountryUnited States
CitySalt Lake City
Period6/23/146/27/14

Fingerprint

Fourier Method
Rational Interpolation
Approximation of Functions
Fast Fourier transform
Domain Decomposition
Approximation
Vertex of a graph
Parallel Implementation
Least Square Method
Fast Fourier transforms
Least Squares
Interpolation
Partition
Polynomials
Decomposition
Unit
Polynomial

ASJC Scopus subject areas

  • Engineering(all)
  • Computational Mathematics
  • Modeling and Simulation
  • Control and Optimization
  • Discrete Mathematics and Combinatorics

Cite this

Platte, R. (2015). A windowed fourier method for approximation of non-periodic functions on equispaced nodes. In Lecture Notes in Computational Science and Engineering (Vol. 106, pp. 405-413). (Lecture Notes in Computational Science and Engineering; Vol. 106). Springer Verlag. https://doi.org/10.1007/978-3-319-19800-2_37

A windowed fourier method for approximation of non-periodic functions on equispaced nodes. / Platte, Rodrigo.

Lecture Notes in Computational Science and Engineering. Vol. 106 Springer Verlag, 2015. p. 405-413 (Lecture Notes in Computational Science and Engineering; Vol. 106).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Platte, R 2015, A windowed fourier method for approximation of non-periodic functions on equispaced nodes. in Lecture Notes in Computational Science and Engineering. vol. 106, Lecture Notes in Computational Science and Engineering, vol. 106, Springer Verlag, pp. 405-413, 10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014, Salt Lake City, United States, 6/23/14. https://doi.org/10.1007/978-3-319-19800-2_37
Platte R. A windowed fourier method for approximation of non-periodic functions on equispaced nodes. In Lecture Notes in Computational Science and Engineering. Vol. 106. Springer Verlag. 2015. p. 405-413. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-319-19800-2_37
Platte, Rodrigo. / A windowed fourier method for approximation of non-periodic functions on equispaced nodes. Lecture Notes in Computational Science and Engineering. Vol. 106 Springer Verlag, 2015. pp. 405-413 (Lecture Notes in Computational Science and Engineering).
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