Search results for "Trilinear interpolation"

showing 4 items of 4 documents

Applications of the Connection between Approximation Theory and Algebra

2009

The aim of this paper is to illustrate a possibility of obtaining various theoretical results using the connection between multivariate interpolation and reduction process with respect to a H-basis of an ideal. Using this connection we can switch between interpolation theory and the theory of ideals. As a application of this connection, we found and proved an interesting identity, which is satisfied for all polynomials in d variables from an interpolation polynomial subspace.

AlgebraComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONTrilinear interpolationBilinear interpolationLinear interpolationBirkhoff interpolationSpline interpolationMathematicsTrigonometric interpolationPolynomial interpolationInterpolation
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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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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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