Konstruktion Mehrdimensionaler B-Splines und Ihre Anwendung auf Approximationsprobleme
The first part of this paper is concerned with the numerical evaluation of multivariate B-splines (cf. ) by means of certain recurrence relations , involving only convex combinations of positive quantities. In the second part facilities of approximating by linear combinations of such B-splines are discussed. In particular, this leads to the construction of linear approximation schemes providing good approximations for a given function as well as for its derivatives of any order (if they exist) lower than the degree of the splines.
Unable to display preview. Download preview PDF.
- 1.Allgower, E. und Georg, K.: Triangulations by reflections with applications to approximation. Numerische Methoden der Approximationstheorie Band 3, ISNM Birkhäuser, Basel-Stuttgart, (1978),Google Scholar
- 4.Dahmen, W.: On multivariate B-splines. Erscheint in SIAM J. Numer. Anal.Google Scholar
- 5.Dahmen, W.: Polynomials as linear combinations of multivariate B-splines. Eingereicht bei Math. Zeitschrift.Google Scholar
- 6.Dahmen, W.: Approximation by linear combinations of multivariate B-splines. In Vorbereitung.Google Scholar
- 7.de Boor, C: Splines as linear combinations of B-splines. A survey in Approximation Theory II, Edited by G.G. Lorentz, C.K. Chui, L.L. Schumaker, Academic Press, 1976, 1–47.Google Scholar
- 11.Micchelli, C.A.: A constructive approach to Kergin interpolation in Rk: Multivariate B-splines and Lagrange interpolation. MRC Technical Summary Report, 1978.Google Scholar
- 12.Morrey, C.B.: Multiple integrals in the calculus of variations. Berlin — Heidelberg — New York, Springer, 1966.Google Scholar