Error analysis in interpolation by bivariate C1-splines

IMA Journal of Numerical Analysis

Volumn 18, Issue 4, 1998, Pages 485-508

  Nurnberger G ^a   Walz, G ^a  

^a UNIVERSITY OF MANNHEIM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY;

ARBITRARY DEGREE; BIVARIATE C; BIVARIATE SPLINE; DATA FITTINGS; HERMITE INTERPOLATION; LAGRANGE INTERPOLATIONS; OPTIMAL APPROXIMATION ORDER; POINT SET;

INTERPOLATION;

EID: 0039835568     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/18.4.485     Document Type: Article

References (13)

1. 1 quadratic bivariate spline interpolation. Numerical Methods of Approximation Theory (ISNM 81) (L. Collatz, G. Meinardus and G. Nürnberger, eds). Basel: Birkhäuser, pp 30-43.
2. CHUI, C. K., & WANG, R. H. 1983 Multivariate spline spaces. J. Math. Anal. Appl. 94, 197-221.
3. CIARLET, P. G. 1978 The Finite Element Method for Elliptic Problems. Amsterdam: North-Holland.
4. n with applications to finite element methods. Arch. Ration. Mech. Anal. 46, 177-199.
5. DAHMEN, W., & MICCHELLI, C. A. 1983 Recent progress in multivariate splines. Approximation Theory IV (C. K. Chui, L. L. Schumaker and J. D. Ward, eds). New York: Academic, pp 27-121.
6. 1 cubic splines on a non-uniform type-2 triangulation of a rectangular domain. C. R. Acad. Sci. Paris Sér. I Math. 314, 413-418.
7. JEEAWOCK-ZEDEK, F., & SABLONNIÈRE, P. 1994 Hermite and Lagrange interpolation by quadratic splines on non-uniform criss-cross triangulations. Wavelets, Images and Surface Fitting (P.-J. Laurent, A. Le Méhauté and L. L. Schumaker, eds). Wellesley: A. K. Peters, pp 445-452.
8. NÜRNBERGER, G. 1994 Approximation by univariate and bivariate splines. Second International Colloquium on Numerical Analysis (D. Bainov and V. Covachev, eds). The Netherlands: VSP Publisher, pp 143-153.
9. NÜRNBERGER, G. 1996 Approximation order of bivariate spline interpolation. J. Approx. Theory 87, 117-136.
10. NÜRNBERGER, G., & RIESSINGER, TH. 1992 Lagrange and Hermite interpolation by bivariate splines. Numer. Funct. Anal. Optimiz. 13, 75-96.
11. NÜRNBERGER, G., & RIESSINGER, TH. 1995 Bivariate spline interpolation at grid points. Numer. Math. 71, 91-119.
12. m,n). Approx. Theory Appl. 1, 71-82.
13. 2. RAIRO Modél. Math. Anal. Numér. 26, 575-593.