Cardinal interpolation by multivariate splines
Authors:
C. K. Chui, K. Jetter and J. D. Ward
Journal:
Math. Comp. 48 (1987), 711724
MSC:
Primary 41A05; Secondary 41A15, 41A63
MathSciNet review:
878701
Fulltext PDF Free Access
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Abstract: The purpose of this paper is to investigate cardinal interpolation using locally supported piecewise polynomials. In particular, the notion of a commutator is introduced and its connection with the Marsden identity is observed. The order of a commutator is shown to be equivalent to the Strang and Fix conditions that arise in the study of the local approximation orders using quasiinterpolants. We also prove that scaled cardinal interpolants give these local approximation orders.
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 J. H. Bramble & S. R. Hilbert, "Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation," SIAM J. Numer. Anal., v. 7, 1970, pp. 112124. MR 0263214 (41:7819)
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 W. Dahmen & C. A. Micchelli, "Translates of multivariate splines," Linear Algebra Appl., v. 52/53, 1983, pp. 217234. MR 709352 (85e:41033)
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 W. Dahmen & C. A. Micchelli, "Recent progress in multivariate splines," in Approximation Theory IV (C. K. Chui, L. L. Schumaker & J. D. Ward, eds.), Academic Press, New York, 1983, pp. 27121. MR 754343 (85h:41013)
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 W. Dahmen & C. A. Micchelli, "On the approximation order from certain multivariate spline spaces," J. Austral. Math. Soc., v. 26, 1984, pp. 233246. MR 765640 (87j:41032)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198708787012
PII:
S 00255718(1987)08787012
Keywords:
Cardinal interpolation,
scaled cardinal interpolation,
Fourier transform,
discrete Fourier transform,
box splines,
Marsden identity
Article copyright:
© Copyright 1987
American Mathematical Society
