Search results for "Nonlinear subdivision"

showing 4 items of 4 documents

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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Improving the stability bound for the PPH nonlinear subdivision scheme for data coming from strictly convex functions

2021

Abstract Subdivision schemes are widely used in the generation of curves and surfaces, and therefore they are applied in a variety of interesting applications from geological reconstructions of unaccessible regions to cartoon film productions or car and ship manufacturing. In most cases dealing with a convexity preserving subdivision scheme is needed to accurately reproduce the required surfaces. Stability respect to the initial input data is also crucial in applications. The so called PPH nonlinear subdivision scheme is proven to be both convexity preserving and stable. The tighter the stability bound the better controlled is the final output error. In this article a more accurate stabilit…

Nonlinear subdivision0209 industrial biotechnologybusiness.industryComputer scienceApplied MathematicsStability (learning theory)020206 networking & telecommunications02 engineering and technologyConvexityComputational MathematicsNonlinear system020901 industrial engineering & automationScheme (mathematics)0202 electrical engineering electronic engineering information engineeringApplied mathematicsVariety (universal algebra)businessConvex functionComputingMethodologies_COMPUTERGRAPHICSSubdivisionApplied Mathematics and Computation
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A nonlinear Chaikin-based binary subdivision scheme

2019

Abstract In this work we introduce and analyze a new nonlinear subdivision scheme based on a nonlinear blending between Chaikin’s subdivision rules and the linear 3-cell subdivision scheme. Our scheme seeks to improve the lack of convergence in the uniform metric of the nonlinear scheme proposed in Amat et al. (2012), where the authors define a cell-average version of the PPH subdivision scheme (Amat et al., 2006). The properties of the new scheme are analyzed and its performance is illustrated through numerical examples.

Nonlinear subdivisionScheme (programming language)business.industryApplied MathematicsMathematicsofComputing_NUMERICALANALYSISBinary numberComputer Science::Computational GeometryComputational MathematicsNonlinear systemMetric (mathematics)Convergence (routing)Applied mathematicsbusinesscomputerComputingMethodologies_COMPUTERGRAPHICSMathematicsSubdivisioncomputer.programming_languageJournal of Computational and Applied Mathematics
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The PCHIP subdivision scheme

2016

In this paper we propose and analyze a nonlinear subdivision scheme based on the monotononicity-preserving third order Hermite-type interpolatory technique implemented in the PCHIP package in Matlab. We prove the convergence and the stability of the PCHIP nonlinear subdivision process by employing a novel technique based on the study of the generalized Jacobian of the first difference scheme. MTM2011-22741

Scheme (programming language)Generalized JacobianStability (learning theory)MathematicsofComputing_NUMERICALANALYSIS010103 numerical & computational mathematics01 natural sciencesConvergence (routing)ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION0101 mathematicsMATLABMathematicscomputer.programming_languageSubdivisionNonlinear subdivision schemesbusiness.industryApplied MathematicsProcess (computing)Approximation order010101 applied mathematicsComputational MathematicsThird orderbusinessConvergencecomputerAlgorithmStability
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