Interpolation by multivariate splines
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- by Charles K. Chui, Harvey Diamond and Louise A. Raphael PDF
- Math. Comp. 51 (1988), 203-218 Request permission
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.References
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C. de Boor, The Polynomials in the Linear Span of Integer Translates of a Compactly Supported Function, MRC Report #2930, April 1986.
- 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
- 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, DOI 10.1090/S0002-9939-1987-0877032-6
- C. K. Chui, K. Jetter, and J. D. Ward, Cardinal interpolation by multivariate splines, Math. Comp. 48 (1987), no. 178, 711–724. MR 878701, DOI 10.1090/S0025-5718-1987-0878701-2
- I. J. Schoenberg, Cardinal spline interpolation, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 12, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. MR 0420078 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.
- Zhen Sha, On interpolation by $S^1_2(\Delta ^{(2)}_{m,n})$, Approx. Theory Appl. 1 (1985), no. 2, 71–82. MR 816602
- Zhen Sha, On interpolation by $S^1_3(\Delta ^{(1)}_{mn})$. I, Approx. Theory Appl. 1 (1985), no. 4, 1–18. MR 885350
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Math. Comp. 51 (1988), 203-218
- MSC: Primary 41A05; Secondary 41A15, 65D07
- DOI: https://doi.org/10.1090/S0025-5718-1988-0942150-X
- MathSciNet review: 942150