140 research outputs found
Optimal spline spaces for -width problems with boundary conditions
In this paper we show that, with respect to the norm, three classes of
functions in , defined by certain boundary conditions, admit optimal
spline spaces of all degrees , and all these spline spaces have
uniform knots.Comment: 17 pages, 4 figures. Fixed a typo. Article published in Constructive
Approximatio
Nodal bases for the serendipity family of finite elements
Using the notion of multivariate lower set interpolation, we construct nodal
basis functions for the serendipity family of finite elements, of any order and
any dimension. For the purpose of computation, we also show how to express
these functions as linear combinations of tensor-product polynomials.Comment: Pre-print of version that will appear in Foundations of Computational
Mathematic
Divided Differences of Implicit Functions
Under general conditions, the equation implicitly defines
locally as a function of . In this article, we express divided differences
of in terms of bivariate divided differences of , generalizing a recent
result on divided differences of inverse functions
Transfinite mean value interpolation in general dimension
AbstractMean value interpolation is a simple, fast, linearly precise method of smoothly interpolating a function given on the boundary of a domain. For planar domains, several properties of the interpolant were established in a recent paper by Dyken and the second author, including: sufficient conditions on the boundary to guarantee interpolation for continuous data; a formula for the normal derivative at the boundary; and the construction of a Hermite interpolant when normal derivative data is also available. In this paper we generalize these results to domains in arbitrary dimension
Transfinite mean value interpolation in general dimension
AbstractMean value interpolation is a simple, fast, linearly precise method of smoothly interpolating a function given on the boundary of a domain. For planar domains, several properties of the interpolant were established in a recent paper by Dyken and the second author, including: sufficient conditions on the boundary to guarantee interpolation for continuous data; a formula for the normal derivative at the boundary; and the construction of a Hermite interpolant when normal derivative data is also available. In this paper we generalize these results to domains in arbitrary dimension
Preferred directions for resolving the non-uniqueness of Delaunay triangulations
AbstractThis note proposes a simple rule to determine a unique triangulation among all Delaunay triangulations of a planar point set, based on two preferred directions. We show that the triangulation can be generated by extending Lawson's edge-swapping algorithm and that point deletion is a local procedure. The rule can be implemented exactly when the points have integer coordinates and can be used to improve image compression methods
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