Bivariate spline interpolation with optimal approximation order

Oleg Davydov, G. Nurnberger, F. Zeilfelder

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

Let be a triangulation of some polygonal domain f c R2 and let S9 (A)
denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181.
LanguageEnglish
Pages181-208
Number of pages28
JournalConstructive Approximation
Volume17
Issue number2
DOIs
Publication statusPublished - 2001

Fingerprint

Bivariate Interpolation
Bivariate Splines
Optimal Approximation
Spline Interpolation
Approximation Order
Splines
Triangulation
Interpolation
Quasi-interpolation
Polynomial Splines
Approximation Error
Hermite
Spline
Triangle
Smoothness
Linearly
Interpolate
Subspace
Denote
Angle

Keywords

  • bivariate spline interpolation
  • optimal approximation
  • mathematical analysis

Cite this

Davydov, Oleg ; Nurnberger, G. ; Zeilfelder, F. / Bivariate spline interpolation with optimal approximation order. In: Constructive Approximation. 2001 ; Vol. 17, No. 2. pp. 181-208.
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Bivariate spline interpolation with optimal approximation order. / Davydov, Oleg; Nurnberger, G.; Zeilfelder, F.

In: Constructive Approximation, Vol. 17, No. 2, 2001, p. 181-208.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Bivariate spline interpolation with optimal approximation order

AU - Davydov, Oleg

AU - Nurnberger, G.

AU - Zeilfelder, F.

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