Results 281 to 290 of about 93,507 (297)

On multivariate Hermite interpolation

Advances in Computational Mathematics, 1995
The authors study the problem of Hermite interpolation by polynomials in several variables. They adopt a very general formulation of this problem, consisting in interpolation of consecutive chains of directional derivatives. By using the notion of blockwise structure introduced by the authors in a previous paper [Math. Comp.
Sauer, Thomas, Xu, Yuan
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Multivariate Pointwise Interpolation

1993
In this chapter, we consider the problem of interpolation of values of a function and its partial derivatives by multivariate polynomials from a certain finite-dimensional space. The interpolation problem consists of the following components: a) the space of polynomials $$\pi (S) = \{ P:P(x) = P({x_1},...,{x_k}) = \sum\limits_{\alpha ...
B. D. Bojanov, H. A. Hakopian, A. A. Sahakian   +2 more
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Multivariate Smoothing and Interpolating Splines

SIAM Journal on Numerical Analysis, 1974
A theorem that characterizes spline functions that both smooth and interpolate is given. A bivariate generalization is presented which permits interpolation and smoothing of information which is not necessarily on a rectangular grid. A theorem which involves reproducing kernels for Hilbert spaces unifies this theory.
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Multivariate Hermite Interpolation on Riemannian Manifolds

SIAM Journal on Scientific Computing
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ralf Zimmermann, Ronny Bergmann
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Optimal Multivariate Interpolation

2005
In this chapter, we are concerned with the problem of multivariate data interpolation. The main focus lies on the concept of minimizing a quadratic form which, in practice, emerges from a physical model, subject to the interpolation constraints. The approach is a natural extension of the one-dimensional polynomial spline interpolation. Besides giving a
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Multivariate Polynomial Interpolation

1990
In this paper, we present multivariate polynomial interpolation methods which are natural extension of the most well-known methods for univariate polynomial interpolation. Special emphasis is put on the Newton approach, and some algorithms of this type are developed in sections 3 and 5.
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Multivariate Mean Value Interpolation

1993
Let T = {t 0 ,... ,t r } ∈ ℝ be an arbitrary set of knots (not necessarily distinct) and µ j := {i : t i = t j } - the multiplicity of the point t j in T. The Hermite interpolant of a function f is defined as a unique polynomial P f µπr (ℝ) satisfying (see Chapter 1) $$P_f^{(m)}({t_j}) = {f^{(m)}}({t_j}),\;m = 0,...,{\mu _j} - 1,\;j = {i_1},{i_2},..
B. D. Bojanov, H. A. Hakopian, A. A. Sahakian   +2 more
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Multivariate Interpolation

1984
G. G. Lorentz, R. A. Lorentz
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Multivariate Periodic Interpolating Wavelets

1995
Nested spaces of multivariate periodic functions are investigated. The scaling functions of these spaces are chosen as fundamental polynomials of Lagrange interpolation on a sparse grid. The interpolatory properties are crucial for the approach based on Boolean sums.
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Multivariable Interpolation Problems

2014
Ph. D.
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