Results 11 to 20 of about 958,747 (333)

Necessary Conditions for Interpolation by Multivariate Polynomials [PDF]

Computational Methods and Function Theory, 2021
Let Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end ...
J. Antezana, J. Marzo, J. Ortega-Cerdà
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MULTIVARIATE AFFINE FRACTAL INTERPOLATION [PDF]

Fractals, 2020
Fractal interpolation functions capture the irregularity of some data very effectively in comparison with the classical interpolants. They yield a new technique for fitting experimental data sampled from real world signals, which are usually difficult to
M. Navascués, S. Katiyar, A. Chand
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On multivariate Lagrange interpolation [PDF]

Mathematics of Computation, 1995
Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions.
Thomas Sauer, Yuan Xu
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Quantum algorithm for multivariate polynomial interpolation [PDF]

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017
How many quantum queries are required to determine the coefficients of a degree-d polynomial in n variables? We present and analyse quantum algorithms for this multivariate polynomial interpolation problem over the fields Fq, R and C. We show that kC and
Jianxin Chen, Andrew M. Childs, S. Hung
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Generalized recursive multivariate interpolation [PDF]

Mathematics of Computation, 1972
A generalized recursive interpolation technique for a set of linear functionals over a set of general univariate basis functions has been previously developed. This paper extends these results to restricted multivariate interpolation over a set of general multivariate basis functions. When the data array is a suitable configuration (e.g., an n
Earl McKinney
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Symmetry in multivariate ideal interpolation

Journal of Symbolic Computation, 2022
An interpolation problem is defined by a set of linear forms on the (multivariate) polynomial ring and values to be achieved by an interpolant. For Lagrange interpolation the linear forms consist of evaluations at some nodes,while Hermite interpolation also considers the values of successive derivatives. Both are examples of ideal interpolation in that
Erick D. Rodríguez Bazan, E. Hubert
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Cardinal interpolation by multivariate splines [PDF]

Mathematics of Computation, 1987
The purpose of this paper is to investigate cardinal interpolation using locally supported piecewise polynomials. In particular, the notion of a commutator is introduced and its connection with the Marsden identity is observed. The order of a commutator is shown to be equivalent to the Strang and Fix conditions that arise in the study of the local ...
Charles K. Chui, Κ. Jetter, J. D. Ward
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Multivariate interpolation: Preserving and exploiting symmetry [PDF]

Journal of Symbolic Computation, 2021
Interpolation is a prime tool in algebraic computation while symmetry is a qualitative feature that can be more relevant to a mathematical model than the numerical accuracy of the parameters. The article shows how to exactly preserve symmetry in multivariate interpolation while exploiting it to alleviate the computational cost.
Erick D. Rodríguez Bazan, E. Hubert
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On the singularity of multivariate Hermite interpolation

Journal of Computational and Applied Mathematics, 2013
In this paper we study the singularity of multivariate Hermite interpolation of type total degree. We present a method to judge the singularity of the interpolation scheme considered and by the method to be developed, we show that all Hermite interpolation of type total degree on $m=d+k$ points in $\R^d$ is singular if $d\geq 2k$. And then we solve the
Zhaoliang Meng, Zhongxuan Luo
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An estimate for multivariate interpolation II

Journal of Approximation Theory, 2006
AbstractSuppose u is a function on a domain Ω in Rn all of whose mth order distributional derivatives are in Lp(Ω) and m is sufficiently large to imply that u is continuous. If the values of u on a sufficiently dense, but not necessarily regular, grid of points are in lp we obtain an estimate of the Lp(Ω) norm of u in terms of the lp norm of these ...
W. R. Madych
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