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On the approximation power of bivariate splines (1998)

Lai, Ming-Jun ; Schumaker, Larry L.

Springer

Advances in computational mathematics 9 (1998), S. 251-279

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ISSN: 1572-9044

Keywords: bivariate splines ; approximation order by splines ; stable approximation schemes ; super-splines ; 41A15 ; 41A63 ; 41A25 ; 65D10

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We show how to construct stable quasi-interpolation schemes in the bivariate spline spaces S d r (Δ) with d⩾ 3r + 2 which achieve optimal approximation order. In addition to treating the usual max norm, we also give results in the L p norms, and show that the methods also approximate derivatives to optimal order. We pay special attention to the approximation constants, and show that they depend only on the smallest angle in the underlying triangulation and the nature of the boundary of the domain.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1018958011262

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