Search results for "Nearest-neighbor interpolation"
showing 7 items of 7 documents
Properties of Generalized Polynomial Spaces in Three Variables
2009
Multivariate interpolation is a topic which often appears in practical modeling problems. Different type of spaces of functions are used for solving interpolation problems. When the interpolation conditions are of different kind, by example, spacial and temporal, one possibility for modeling the problem is to use a generalize degree, in which the monomials exponents are weighted with a weight vector with integer components. In order to use such a generalize polynomial space as interpolation space, it is necessary to know the dimension and a basis of it. The aim of this article is to study and prove many properties of the generalize polynomial spaces in three variables.
Temperature interpolation by local information ; the example of France
2010
International audience; Methods of interpolation, whether based on regressions or on kriging, are global methods in which all the available data for a given study area are used. But the quality of results is affected when the study area is spatially very heterogeneous. To overcome this difficulty, a method of local interpolation is proposed and tested here with temperature in France. Starting from a set of weather stations spread across the country and digitized as 250 m-sided cells, the method consists in modelling local spatial variations in temperature by considering each point of the grid and the n weather stations that are its nearest neighbours. The procedure entails a series of steps…
The λ-Error Order in Multivariate Interpolation
2005
The aim of this article is to introduce and to study a generalization of the error order of interpolation, named λ – error order of interpolation. This generalization makes possible a deeper analysis of the error in the interpolation process. We derived the general form of the λ – error order of interpolation and then we applied it for many choices of the functional λ.
Error bounds for a convexity-preserving interpolation and its limit function
2008
AbstractError bounds between a nonlinear interpolation and the limit function of its associated subdivision scheme are estimated. The bounds can be evaluated without recursive subdivision. We show that this interpolation is convexity preserving, as its associated subdivision scheme. Finally, some numerical experiments are presented.
Hermite interpolation: The barycentric approach
1991
The barycentric formulas for polynomial and rational Hermite interpolation are derived; an efficient algorithm for the computation of these interpolants is developed. Some new interpolation principles based on rational interpolation are discussed.
Reconstructions that combine interpolation with least squares fitting
2015
We develop a reconstruction that combines interpolation and least squares fitting for point values in the context of multiresolution a la Harten. We study the smoothness properties of the reconstruction as well as its approximation order. We analyze how different adaptive techniques (ENO, SR and WENO) can be used within this reconstruction. We present some numerical examples where we compare the results obtained with the classical interpolation and the interpolation combined with least-squares approximation. We develop a reconstruction that combines interpolation and least squares fitting.We study the smoothness properties of the reconstruction and its approximation order.We present some nu…
Discrete multiresolution based on hermite interpolation: computing derivatives
2004
Abstract Harten’s framework for multiresolution representation of data has been extended by Warming and Beam in [SIAM J. Sci. Comp. 22 (2000) 1269] to include Hermite interpolation. It needs the point-values of the derivative, which are usually unavailable, so they have to be approximated. In this work we show that the way in which the derivatives are approximated is crucial for the success of the method, and we present a new way to compute them that makes the scheme adequate for non-smooth data.