Translates of multivarlate splines
TLDR
In this paper, the authors study spaces generated by translations of a fixed function over lattice points and provide algebraic and approximation properties for these spaces which show their applicability for finite element analysis.About:
This article is published in Linear Algebra and its Applications.The article was published on 1983-07-01 and is currently open access. It has received 132 citations till now. The article focuses on the topics: Algebraic number & Finite element method.read more
Citations
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Journal ArticleDOI
Error estimates and condition numbers for radial basis function interpolation
TL;DR: A variation of the Narcowich-Ward theory of upper bounds on the norm of the inverse of the interpolation matrix is presented in order to handle the whole set of radial basis functions that are currently in use.
Book
Box Splines
TL;DR: A brief introduction to box and half-box splines with particular focus on triangular splines and surface design is given in this paper, where the B-splines with equidistant knots are considered.
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Approximation from shift-invariant subspaces of $L\sb 2(\bold R\sp d)$
Book ChapterDOI
Using the refinement equations for the construction of Pre-Wavelets II: powers and two
TL;DR: The notion of extensibility of a finite set of Laurent polynomials is shown to be central in the construction of wavelet decompositions by decomposition of spaces in a multiresolution analysis.
Journal ArticleDOI
Approximation by superposition of sigmoidal and radial basis functions
TL;DR: In this paper, it was shown that unless @s is itself a polynomial, it is possible to uniformly approximate any continuous function on R^s arbitrarily well on every compact subset of R^ s by functions in this span.
References
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Contributions to the problem of approximation of equidistant data by analytic functions. Part A. On the problem of smoothing or graduation. A first class of analytic approximation formulae
Journal ArticleDOI
Contributions to the problem of approximation of equidistant data by analytic functions. Part B. On the problem of osculatory interpolation. A second class of analytic approximation formulae
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B-Splines From Parallelepipeds.
C. de Boor,Klaus Hoellig +1 more
TL;DR: This note is a first attempt in this direction and deals with basic approximation properties of translates of one box-splines such as stability, degree of approximation etc.