Interpolation by multivariate splines

Authors:
Charles K. Chui, Harvey Diamond and Louise A. Raphael

Journal:
Math. Comp. **51** (1988), 203-218

MSC:
Primary 41A05; Secondary 41A15, 65D07

MathSciNet review:
942150

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Abstract | References | Similar Articles | Additional Information

Abstract: A general interpolation scheme by multivariate splines at regular sample points is introduced. This scheme guarantees the local optimal order of approximation to sufficiently smooth data functions. A discussion on numerical implementation is included.

**[1]**C. de Boor,*The Polynomials in the Linear Span of Integer Translates of a Compactly Supported Function*, MRC Report #2930, April 1986.**[2]**Carl de Boor, Klaus Höllig, and Sherman Riemenschneider,*Bivariate cardinal interpolation by splines on a three-direction mesh*, Illinois J. Math.**29**(1985), no. 4, 533–566. MR**806466****[3]**Charles K. Chui and Harvey Diamond,*A natural formulation of quasi-interpolation by multivariate splines*, Proc. Amer. Math. Soc.**99**(1987), no. 4, 643–646. MR**877032**, 10.1090/S0002-9939-1987-0877032-6**[4]**C. K. Chui, K. Jetter, and J. D. Ward,*Cardinal interpolation by multivariate splines*, Math. Comp.**48**(1987), no. 178, 711-724. MR**878701**, 10.1090/S0025-5718-1987-0878701-2**[5]**I. J. Schoenberg,*Cardinal spline interpolation*, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 12. MR**0420078****[6]**G. Strang & G. Fix, "A Fourier analysis of the finite element variational method," C.I.M.E. II Ciclo 1971,*Constructive Aspects of Functional Analysis*(G. Geymonat, ed.), 1973, pp. 793-840.**[7]**Zhen Sha,*On interpolation by 𝑆¹₂(Δ⁽²⁾_{𝑚,𝑛})*, Approx. Theory Appl.**1**(1985), no. 2, 71–82. MR**816602****[8]**Zhen Sha,*On interpolation by 𝑆¹₃(Δ⁽¹⁾_{𝑚𝑛}). I*, Approx. Theory Appl.**1**(1985), no. 4, 1–18. MR**885350**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0942150-X

Keywords:
Multivariate splines,
interpolation,
optimal order,
box splines,
fundamental function,
numerical implementation

Article copyright:
© Copyright 1988
American Mathematical Society