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Volume 50, Issue 2
A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods

Li-Lian Wang

DOI: 10.4208/jms.v50n2.17.01

J. Math. Study, 50 (2017), pp. 101-143.

Published online: 2017-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

This paper is devoted to a review of the prolate spheroidal wave functions (PSWFs) and their variants from the viewpoint of spectral ⁄ spectral-element approximations using such functions as basis functions. We demonstrate the pros and cons over their polynomial counterparts, and put the emphasis on the construction of essential building blocks for efficient spectral algorithms.

  • Keywords

Prolate spheroidal wave functions and their generalisations, time-frequency concentration problem, bandlimited functions, finite Fourier ⁄ Hankel transforms, quasi-uniform grids, well-conditioned prolate collocation scheme, prolate-Galerkin method, spectral accuracy.

  • AMS Subject Headings

33C47, 33E30, 41A30, 42C05, 65D32, 65N35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lilian@ntu.edu.sg (Li-Lian Wang)

  • BibTex
  • RIS
  • TXT
@Article{JMS-50-101, author = {Wang , Li-Lian}, title = {A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods}, journal = {Journal of Mathematical Study}, year = {2017}, volume = {50}, number = {2}, pages = {101--143}, abstract = {

This paper is devoted to a review of the prolate spheroidal wave functions (PSWFs) and their variants from the viewpoint of spectral ⁄ spectral-element approximations using such functions as basis functions. We demonstrate the pros and cons over their polynomial counterparts, and put the emphasis on the construction of essential building blocks for efficient spectral algorithms.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v50n2.17.01}, url = {http://global-sci.org/intro/article_detail/jms/10005.html} }
TY - JOUR T1 - A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods AU - Wang , Li-Lian JO - Journal of Mathematical Study VL - 2 SP - 101 EP - 143 PY - 2017 DA - 2017/06 SN - 50 DO - http://doi.org/10.4208/jms.v50n2.17.01 UR - https://global-sci.org/intro/article_detail/jms/10005.html KW - Prolate spheroidal wave functions and their generalisations, time-frequency concentration problem, bandlimited functions, finite Fourier ⁄ Hankel transforms, quasi-uniform grids, well-conditioned prolate collocation scheme, prolate-Galerkin method, spectral accuracy. AB -

This paper is devoted to a review of the prolate spheroidal wave functions (PSWFs) and their variants from the viewpoint of spectral ⁄ spectral-element approximations using such functions as basis functions. We demonstrate the pros and cons over their polynomial counterparts, and put the emphasis on the construction of essential building blocks for efficient spectral algorithms.

Wang , Li-Lian. (2017). A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods. Journal of Mathematical Study. 50 (2). 101-143. doi:10.4208/jms.v50n2.17.01
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