Mathematics of Computation

Author(s): Huiyuan Li; Yuan Xu.
Journal: Math. Comp.
MSC (2000): Primary 41A05, 41A10
Posted: August 27, 2008
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Abstract: A discrete Fourier analysis on the dodecahedron is studied, from which results on a tetrahedron are deduced by invariance. The results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains. In particular, a trigonometric Lagrange interpolation on the tetrahedron is shown to satisfy an explicit compact formula and the Lebesgue constant of the interpolation is shown to be in the order of $(\log n)^3$ .

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Huiyuan Li
Affiliation: Institute of Software, Chinese Academy of Sciences, Beijing 100190, China
Email: hynli@mail.rdcps.ac.cn

Yuan Xu
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222.
Email: yuan@math.uoregon.edu

DOI: 10.1090/S0025-5718-08-02156-X
PII: S 0025-5718(08)02156-X
Keywords: Discrete Fourier series, trigonometric, Lagrange interpolation, dodecahedron, tetrahedron
Received by editor(s): April 10, 2007
Received by editor(s) in revised form: February 29, 2008
Posted: August 27, 2008
Additional Notes: The first authors were supported by NSFC Grants 10601056, 10431050 and 60573023. The second author was supported by NSF Grant DMS-0604056
Copyright of article: Copyright 2008, American Mathematical Society

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