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.

AlgebraNearest-neighbor interpolationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONInterpolation spaceLinear interpolationBirkhoff interpolationSpline interpolationMathematicsTrigonometric interpolationInterpolationPolynomial interpolation
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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…

Atmospheric Science010504 meteorology & atmospheric sciencesbusiness.industrytemperature[SHS.GEO]Humanities and Social Sciences/Geography010501 environmental sciences01 natural sciencesinterpolationMultivariate interpolation[ SHS.GEO ] Humanities and Social Sciences/GeographyNearest-neighbor interpolation13. Climate actionKrigingPolygonStatisticsLinear regressionSpatial variabilityFrancebusiness0105 earth and related environmental sciencesSubdivisionMathematicsInterpolation
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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.

Discrete mathematicsNearest-neighbor interpolationMathematicsofComputing_NUMERICALANALYSISTrilinear interpolationApplied mathematicsBilinear interpolationStairstep interpolationLinear interpolationSpline interpolationComputingMethodologies_COMPUTERGRAPHICSMultivariate interpolationInterpolationMathematics
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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.

Mathematical optimizationNonlinear subdivision schemesbusiness.industryApplied MathematicsNumerical analysisMathematicsofComputing_NUMERICALANALYSISStairstep interpolationComputer Science::Computational GeometryConvexityMultivariate interpolationComputational MathematicsError boundsComputer Science::GraphicsNearest-neighbor interpolationTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONApplied mathematicsComputer Science::Symbolic ComputationConvexity preservingbusinessSpline interpolationSubdivisionInterpolationMathematicsComputingMethodologies_COMPUTERGRAPHICSJournal of Computational and Applied Mathematics
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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.

Numerical AnalysisMathematical analysisComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONMathematicsofComputing_NUMERICALANALYSISTrilinear interpolationStairstep interpolationBirkhoff interpolationComputer Science ApplicationsTheoretical Computer SciencePolynomial interpolationComputational MathematicsComputational Theory and MathematicsNearest-neighbor interpolationHermite interpolationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONApplied mathematicsSpline interpolationSoftwareComputingMethodologies_COMPUTERGRAPHICSMathematicsInterpolationComputing
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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…

Numerical AnalysisMathematical optimizationApplied MathematicsTrilinear interpolationBilinear interpolationStairstep interpolationLinear interpolationMultivariate interpolationComputational MathematicsNearest-neighbor interpolationApplied mathematicsSpline interpolationMathematicsInterpolationApplied Numerical Mathematics
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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.

Numerical AnalysisMathematical optimizationHermite splineApplied MathematicsMonotone cubic interpolationBirkhoff interpolationMultivariate interpolationCubic Hermite splineNearest-neighbor interpolationHermite interpolationModeling and SimulationApplied mathematicsMathematicsInterpolationCommunications in Nonlinear Science and Numerical Simulation
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