On Stable Local Bases for Bivariate Polynomial Spline Spaces
نویسندگان
چکیده
منابع مشابه
On Stable Local Bases for Bivariate Polynomial Spline Spaces
Stable locally supported bases are constructed for the spaces S r d (4) of polynomial splines of degree d 3r + 2 and smoothness r deened on trian-gulations 4, as well as for various superspline subspaces. In addition, we show that for r 1, it is impossible to construct bases which are simultaneously stable and locally linearly independent. x1. Introduction This paper deals with the classical sp...
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Locally linearly independent bases are constructed for the spaces S r d (4) of polynomial splines of degree d 3r + 2 and smoothness r deened on triangulations, as well as for their superspline subspaces. x1. Introduction Given a regular triangulation 4 of a set of vertices V, let S r d (4) := fs 2 C r (() : sj T 2 P d for all triangles T 2 4g; where P d is the space of polynomials of degree d, ...
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We derive L 1 bounds for norms of projections onto bivariate polynomial spline spaces on regular triangulations with stable local bases. We then apply this result to derive error bounds for best L 2-and`2-approximation by splines on quasi-uniform triangulations. x1. Introduction Let X L 1 (() be a linear space deened a set with polygonal boundary. Suppose hh; i is a semi-deenite inner-product o...
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We give a stable construction of local nodal bases for spaces of C 1 bivariate polynomial splines of degree d 5 deened on arbitrary tri-angulations. The bases given here diier from recently constructed locally linearly independent bases, and in fact we show that stability and local linear independence cannot be achieved simultaneously. x1. Introduction Given a regular triangulation 4, let S r d...
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Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...
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ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2001
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-001-0006-8