Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Bivariate interpolation with quadratic box splines
HTML articles powered by AMS MathViewer

by Morten Dæhlen and Tom Lyche PDF
Math. Comp. 51 (1988), 219-230 Request permission

Abstract:

Existence and uniqueness results are given for interpolation with translates of a bivariate, three-directional, ${C^0}$-quadratic box spline over a finite polygonal region. A Hermite interpolation problem for a slightly more general box spline is also considered.
References
  • C. de Boor and K. Höllig, Bivariate box splines and smooth pp functions on a three direction mesh, J. Comput. Appl. Math. 9 (1983), no. 1, 13–28. MR 702228, DOI 10.1016/0377-0427(83)90025-0
  • Carl de Boor, Multivariate approximation, The state of the art in numerical analysis (Birmingham, 1986) Inst. Math. Appl. Conf. Ser. New Ser., vol. 9, Oxford Univ. Press, New York, 1987, pp. 87–109. MR 921663
  • E. Ward Cheney, Multivariate approximation theory, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 51, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1986. Selected topics. MR 862115, DOI 10.1137/1.9781611970197
    • C. K. Chui, T. X. He & R. H. Wang, "Interpolation of bivariate linear splines," in Alfred Haar Memorial Conference (J. Szabados and K. Tandori, eds.), North-Holland, Amsterdam, 1986.
  • C. K. Chui and T. X. He, On location of sample points for interpolation by bivariate $C^1$ quadratic splines, Numerical methods of approximation theory, Vol. 8 (Oberwolfach, 1986) Internat. Schriftenreihe Numer. Math., vol. 81, Birkhäuser, Basel, 1987, pp. 30–43. MR 1025765
  • Morten Dæhlen, An example of bivariate interpolation with translates of $C^0$-quadratic box-splines on a three direction mesh, Comput. Aided Geom. Design 4 (1987), no. 3, 251–255. MR 917785, DOI 10.1016/0167-8396(87)90017-3
  • Klaus Höllig, Box splines, Approximation theory, V (College Station, Tex., 1986) Academic Press, Boston, MA, 1986, pp. 71–95. MR 903683
  • Charles A. Micchelli, Algebraic aspects of interpolation, Approximation theory (New Orleans, La., 1986) Proc. Sympos. Appl. Math., vol. 36, Amer. Math. Soc., Providence, RI, 1986, pp. 81–102. MR 864367, DOI 10.1090/psapm/036/864367
    • T. I. Mueller, Geometric Modelling with Multivariate B-splines, Dissertation, Dept. of Comp. Sci., Univ. of Utah, 1986.
  • Kurt Jetter, A short survey on cardinal interpolation by box splines, Topics in multivariate approximation (Santiago, 1986) Academic Press, Boston, MA, 1987, pp. 125–139. MR 924827
  • Larry L. Schumaker, Spline functions: basic theory, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1981. MR 606200
  • Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502
Similar Articles
Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 51 (1988), 219-230
  • MSC: Primary 41A05; Secondary 41A15, 65D07
  • DOI: https://doi.org/10.1090/S0025-5718-1988-0942151-1
  • MathSciNet review: 942151