منابع مشابه
Local cohomology of bivariate splines
We consider the problem of determining the dimension of the space of bivariate splines C k( ), for all k. This problem is closely related to the question of whether C(̂) is a free R-module. The main result is that C(̂) is free if and only if j j has genus zero and C k( ) has the expected dimension for k = r + 1 (and hence for all k). We also obtain several interesting corollaries, including the...
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In this paper we continue our earlier research [4] aimed at developing efficient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used in [5], a hybrid polynomial/radial basis scheme was considered in [4], where the local knot locations for the RBF terms w...
متن کاملLocal Lagrange Interpolation by Bivariate C 1 Cubic Splines
Lagrange interpolation schemes are constructed based on C 1 cubic splines on certain triangulations obtained from checkerboard quad-rangulations. x1. Introduction Given a triangulation 4 of a simply connected polygonal domain , the space of C 1 cubic splines is deened by S 1 3 (4) := fs 2 C 1 (() : sj T 2 P 3 , all T 2 4g; where P 3 is the space of cubic bivariate polynomials. In this paper we ...
متن کاملLocal hybrid approximation for scattered data fitting with bivariate splines
We suggest a local hybrid approximation scheme based on polynomials and radial basis functions, and use it to improve the scattered data fitting algorithm of [7]. Similar to that algorithm, the new method has linear computational complexity and is therefore suitable for large real world data. Numerical examples suggest that it can produce high quality artifact–free approximations that are more ...
متن کاملStable Local Nodal Bases for C 1 Bivariate Polynomial Splines
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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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1997
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(97)00026-1