Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Multivariate piecewise polynomials
View through CrossRef
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.
Title: Multivariate piecewise polynomials
Description:
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.
Related Results
Truncated-Exponential-Based Appell-Type Changhee Polynomials
Truncated-Exponential-Based Appell-Type Changhee Polynomials
The truncated exponential polynomials em(x) (1), their extensions, and certain newly-introduced polynomials which combine the truncated exponential polynomials with other known pol...
Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function
Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function
The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and ...
Krein–Sobolev Orthogonal Polynomials II
Krein–Sobolev Orthogonal Polynomials II
In a recent paper, Littlejohn and Quintero studied the orthogonal polynomials {Kn}n=0∞—which they named Krein–Sobolev polynomials—that are orthogonal in the classical Sobolev space...
On λ-Changhee–Hermite polynomials
On λ-Changhee–Hermite polynomials
Abstract
In this paper, we introduce a new class of
λ-analogues of the Changhee–Hermite polynomials and
generalized Gould–Hopper–Appell type λ-Changhee polynomials,
...
A METHOD FOR ADJUSTING THE FIRING VECTOR WHEN BUILDING PIECEWISE LINEAR REGRESSION MODELS
A METHOD FOR ADJUSTING THE FIRING VECTOR WHEN BUILDING PIECEWISE LINEAR REGRESSION MODELS
The paper provides a brief overview of publications related to the construction and analysis of nonlinear regression models. Specifically, it considers the following topics: a piec...
Robust H∞ Feedback Compensator Design for Linear Parabolic DPSs with Pointwise/Piecewise Control and Pointwise/Piecewise Measurement
Robust H∞ Feedback Compensator Design for Linear Parabolic DPSs with Pointwise/Piecewise Control and Pointwise/Piecewise Measurement
In this paper, a robust H∞ control problem of a class of linear parabolic distributed parameter systems (DPSs) with pointwise/piecewise control and pointwise/piecewise measurement ...
Mittag-Leffler-Gould-Hopper polynomials: Symbolic Approach
Mittag-Leffler-Gould-Hopper polynomials: Symbolic Approach
The paper describes the method of symbolic evaluation that serves as a
useful tool to extend the studies of certain special functions including
their properties and capabilities. I...
Superring of Polynomials over a Hyperring
Superring of Polynomials over a Hyperring
A Krasner hyperring (for short, a hyperring) is a generalization of a ring such that the addition is multivalued and the multiplication is as usual single valued and satisfies the ...