Multivariate spline spaces

2001 ◽  
pp. 27-118
Author(s):  
Ren-Hong Wang
Keyword(s):  
Multivariate Spline

scholarly journals Approximation of noisy data using multivariate splines and finite element methods

2021 ◽  
Vol 15 ◽  
pp. 174830262110084
Author(s):  
Bishnu P Lamichhane ◽  
Elizabeth Harris ◽  
Quoc Thong Le Gia
Keyword(s):  
Finite Element ◽  
Differential Operators ◽  
Impulsive Noise ◽  
Noisy Data ◽  
Multivariate Splines ◽  
The Finite Element Method ◽  
Data Smoothing ◽  
Multivariate Spline ◽  
Partial Differential Operators ◽  
Mixture Of Gaussian

We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares functional. The penalties are based on partial differential operators, and are integrated using the finite element method. We compare three methods to two problems: to remove the mixture of Gaussian and impulsive noise from an image, and to recover a continuous function from a set of noisy observations.

Multivariate piecewise polynomials

Acta Numerica ◽  
1993 ◽  
Vol 2 ◽  
pp. 65-109 ◽  
Author(s):  
C. de Boor
Keyword(s):  
Approximation Theory ◽  
Variational Approach ◽  
Polynomial Function ◽  
Piecewise Polynomial ◽  
Multivariate Splines ◽  
Piecewise Polynomial Function ◽  
Multivariate Spline ◽  
Piecewise Polynomials ◽  
The Subject ◽  
Function Of Several Arguments

This article was supposed to be on ‘multivariate splines». An informal survey, taken recently by asking various people in Approximation Theory what they consider to be a ‘multivariate spline’, resulted in the answer that a multivariate spline is a possibly smooth piecewise polynomial function of several arguments. In particular the potentially very useful thin-plate spline was thought to belong more to the subject of radial basis funtions than in the present article. This is all the more surprising to me since I am convinced that the variational approach to splines will play a much greater role in multivariate spline theory than it did or should have in the univariate theory. Still, as there is more than enough material for a survey of multivariate piecewise polynomials, this article is restricted to this topic, as is indicated by the (changed) title.

scholarly journals On the approximation order from certain multivariate spline spaces

1984 ◽  
Vol 26 (2) ◽  
pp. 233-246 ◽  
Author(s):  
Wolfgang Dahmen ◽  
Charles A. Micchelli
Keyword(s):  
Approximation Order ◽  
Bivariate Splines ◽  
Multivariate Spline ◽  
Approximation Rates

AbstractIn this paper, we determine the optimal controlled approximation rates from certain bivariate splines on regular meshes.

scholarly journals Multivariate spline approximation of the signed distance function

2014 ◽  
Vol 265 ◽  
pp. 276-289 ◽  
Author(s):  
Ren-Hong Wang ◽  
Qing-Jie Guo ◽  
Chun-Gang Zhu ◽  
Chun-Jing Li
Keyword(s):  
Distance Function ◽  
Spline Approximation ◽  
Signed Distance Function ◽  
Multivariate Spline ◽  
Signed Distance

scholarly journals Multivariate spline space over cross-cut partition

2007 ◽  
Vol 54 (3) ◽  
pp. 415-426 ◽  
Author(s):  
Ren-Hong Wang ◽  
Feng-Gong Lang
Keyword(s):  
Spline Space ◽  
Multivariate Spline

scholarly journals Stable Local Bases for Multivariate Spline Spaces

2001 ◽  
Vol 111 (2) ◽  
pp. 267-297 ◽  
Author(s):  
Oleg Davydov
Keyword(s):  
Multivariate Spline
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