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Analysis of spectral approximations using prolate spheroidal wave functions
Author(s):
Li-Lian
Wang.
Journal:
Math. Comp.
79
(2010),
807-827.
MSC (2000):
Primary 65N35, 65N22, 65F05, 35J05
Posted:
September 17, 2009
MathSciNet review:
2600544
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Abstract:
In this paper, the approximation properties of the prolate spheroidal wave functions of order zero (PSWFs) are studied, and a set of optimal error estimates are derived for the PSWF approximation of non-periodic functions in Sobolev spaces. These results serve as an indispensable tool for the analysis of PSWF spectral methods. A PSWF spectral-Galerkin method is proposed and analyzed for elliptic-type equations. Illustrative numerical results consistent with the theoretical analysis are also presented.
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Additional Information:
Li-Lian
Wang
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
Email:
lilian@ntu.edu.sg
DOI:
10.1090/S0025-5718-09-02268-6
PII:
S 0025-5718(09)02268-6
Keywords:
Prolate spheroidal wave functions,
bandlimited functions,
approximations in Sobolev spaces,
spectral methods,
quasi-uniform grids
Received by editor(s):
July 16, 2008
Received by editor(s) in revised form:
December 30, 2008
Posted:
September 17, 2009
Additional Notes:
This work is partially supported by AcRF Tier 1 Grant RG58/08, Singapore MOE Grant T207B2202, and Singapore NRF2007IDM-IDM002-010.
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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