Quasi-interpolation projectors for box splines

Journal of Computational and Applied Mathematics

Volumn 221, Issue 2, 2008, Pages 416-429

  Lyche, Tom ^a   Manni, Carla ^b   Sablonnière, Paul ^c  

^a UNIVERSITY OF OSLO   (Norway)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

^c INSA DE RENNES   (France)

Author keywords

Box splines; Projectors; Quasi interpolation

Indexed keywords

BOX SPLINES; INTERPOLANTS; LOCAL LINEAR; PROJECTORS; QUASI-INTERPOLATION; SPLINE SPACE;

SPLINES;

EID: 52149092353     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.10.029     Document Type: Article

References (20)

1. D. Barrera, Esquemas locales de interpolación de Lagrange y Hermite. Su extensión a dos variables. Tesis doctoral. Universidad de Granada, 1997
2. Bojanov B.D., Hakopian H.A., and Sahakian A.A. Spline Functions and Multivariate Interpolations (1993), Kluwer
3. de Boor C. Quasi interpolants and approximation power of multivariate splines. In: Dahmen W., Gasca M., and Micchelli C.A. (Eds). Computation of Curves and Surfaces (1990), Kluwer 313-345
4. de Boor C., Höllig K., and Riemenschneider S. Some qualitative properties of bivariate Euler-Frobenius polynomials. J. Approx. Theory 50 (1987) 8-17
5. de Boor C., Höllig K., and Riemenschneider S. Box Splines (1993), Springer, Berlin
6. Chui C.K., and Diamond H. A natural formulation of quasi-interpolation by multivariate splines. Proc. Amer. Math. Soc. 99 (1987) 643-646
7. C.K. Chui, H. Diamond, L. Raphael, Convexity preserving quasi-interpolation and interpolation by box spline surfaces, in: Transactions of the Fifth Army Conference on Applied Mathematics and Computing, U.S. Army Res. Office, Research Triangle Park, NC, 1988, pp. 301-310
8. Chui C.K., and Lai M.J. Algorithms for generating B-nets and graphically displaying spline surfaces on three and four-directional meshes. Comput. Aided Geom. Design 8 (1991) 479-493
9. Chui C.K., and Lai M.-J. A multivariate analog of Marsden's identity and a quasi-interpolation scheme. Constr. Approx. 3 (1987) 111-122
10. Dæhlen M., and Lyche T. Box splines and applications. In: Hagen H., and Roller D. (Eds). Geometric Modelling: Methods and Applications (1991), Springer Verlag, Berlin 35-93
11. Dahmen W., and Micchelli C.A. On the multivariate Euler-Frobenius polynomials. In: Sendov B., Petrushev P., Malev R., and Tashev S. (Eds). Constructive Theory of Functions'84 (1984), Bulgarian Academy of Sciences, Sofia 237-243
12. Lee B.-G., Lyche T., and Mørken K. Some examples of quasi-interpolants constructed from local spline projectors. In: Lyche T., and Schumaker L.L. (Eds). Mathematical Methods for Curves and Surfaces; Oslo 2000 (2001), Vanderbilt Univ. Press, Nashville, TN
13. Lyche T., and Schumaker L.L. Local spline approximation methods. J. Approx. Theory 4 (1975) 294-325
14. Micchelli C.A. Banded matrices with banded inverses. J. Comput. Appl. Math. 41 (1992) 281-300
15. s: Compactly supported fundamental solutions. Numer. Math. 70 (1995) 331-351
16. P. Sablonnière, A catalog of B-splines of degree ≤ 10 on a three direction mesh, Publication No 132 du Laboratoire Analyse Numérique et Optimisation, Université de Lille, 1984
17. Sablonnière P. Quasi-interpolants associated with H-splines on a three-direction mesh. J. Comput. Appl. Math. 66 (1996) 433-442
18. Sablonnière P. H-splines and quasi-interpolants on a three-directional mesh. In: Buhmann M., and Mache D. (Eds). Advanced Topics in Constructive Approximation. ISNM vol. 142 (2002), Birkhäuser 187-201
19. Sablonnière P. Recent progress on univariate and multivariate polynomial or spline quasi-interpolants. In: de Brujn M.G., Mache D.H., and Szabadoz J. (Eds). Trends and Applications in Constructive Approximation. ISNM vol. 151 (2005), Birhäuser Verlag, Basel 229-245
20. Wang R.H. Multivariate Spline Functions and Their Applications (2001), Kluwer, Dordrecht