Search results for "Stairstep interpolation"

showing 5 items of 5 documents

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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A nonlinear algorithm for monotone piecewise bicubic interpolation

2016

We present an algorithm for monotone interpolation on a rectangular mesh.We use the sufficient conditions for monotonicity of Carlton and Fritsch.We use nonlinear techniques to approximate the partial derivatives at the grid points.We develop piecewise bicubic Hermite interpolants with these approximations.We present some numerical examples where we compare different results. In this paper we present an algorithm for monotone interpolation of monotone data on a rectangular mesh by piecewise bicubic functions. Carlton and Fritsch (1985) develop conditions on the Hermite derivatives that are sufficient for such a function to be monotone. Here we extend our results of Arandiga (2013) to obtain…

Hermite polynomialsApplied MathematicsMathematical analysisMonotone cubic interpolationStairstep interpolation010103 numerical & computational mathematics02 engineering and technology01 natural sciencesComputational MathematicsComputer Science::GraphicsMonotone polygon0202 electrical engineering electronic engineering information engineeringPiecewisePartial derivativeBicubic interpolation020201 artificial intelligence & image processing0101 mathematicsMathematicsInterpolationApplied Mathematics and Computation
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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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