Search results for "MathematicsofComputing_NUMERICALANALYSIS"

showing 10 items of 149 documents

A generalized integration formula for indefinite integrals of special functions

2020

An integration formula for generating indefinite integrals which was presented in Conway JT [A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec...

Differential equationApplied Mathematics010102 general mathematicsMathematicsofComputing_NUMERICALANALYSIS010103 numerical & computational mathematicsIntegral transform01 natural sciencesAlgebraVDP::Teknologi: 500symbols.namesakeTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESSpecial functionsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONsymbols0101 mathematicsAnalysisLagrangianMathematicsIntegral Transforms and Special Functions
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Weighted Extrapolation Techniques for Finite Difference Methods on Complex Domains with Cartesian Meshes

2016

The design of numerical boundary conditions in high order schemes is a challenging problem that has been tackled in different ways depending on the nature of the problem and the scheme used to solve it numerically. In this paper we propose a technique to extrapolate the information from the computational domain to ghost cells for schemes with structured Cartesian Meshes on complex domains. This technique is based on the application of Lagrange interpolation with weighted filters for the detection of discontinuities that permits a data dependent extrapolation, with high order at smooth regions and essentially non oscillatory properties near discontinuities. This paper is a sequel of Baeza et…

Discrete mathematicsComputer scienceMathematicsofComputing_NUMERICALANALYSISExtrapolationFinite difference methodLagrange polynomialBoundary (topology)Classification of discontinuitieslaw.inventionsymbols.namesakelawsymbolsApplied mathematicsPolygon meshCartesian coordinate systemBoundary value problem
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Tensor product multiresolution analysis with error control for compact image representation

2002

A class of multiresolution representations based on nonlinear prediction is studied in the multivariate context based on tensor product strategies. In contrast to standard linear wavelet transforms, these representations cannot be thought of as a change of basis, and the error induced by thresholding or quantizing the coefficients requires a different analysis. We propose specific error control algorithms which ensure a prescribed accuracy in various norms when performing such operations on the coefficients. These algorithms are compared with standard thresholding, for synthetic and real images.

Discrete mathematicsMultiresolution analysisMathematicsofComputing_NUMERICALANALYSISWavelet transformImage processingReal imageThresholdingTensor productControl and Systems EngineeringSignal ProcessingComputer Vision and Pattern RecognitionElectrical and Electronic EngineeringChange of basisAlgorithmSoftwareMathematicsImage compressionSignal Processing
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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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Weighted-Power p Nonlinear Subdivision Schemes

2012

In this paper we present and analyze a generalization of the Powerp subdivision schemes proposed in [3,12]. The Weighted-Powerp schemes are based on a harmonic weighted version of the Power<emp average considered in [12], and their development is motivated by the desire to generalize the nonlinear analysis in [3,5] to interpolatory subdivision schemes with higher than second order accuracy.

Discrete mathematicsNonlinear systemGeneralizationbusiness.industryConvergence (routing)MathematicsofComputing_NUMERICALANALYSISStability (learning theory)Order (group theory)Harmonic (mathematics)businessMathematicsPower (physics)Subdivision
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An exact and efficient approach for computing a cell in an arrangement of quadrics

2006

AbstractWe present an approach for the exact and efficient computation of a cell in an arrangement of quadric surfaces. All calculations are based on exact rational algebraic methods and provide the correct mathematical results in all, even degenerate, cases. By projection, the spatial problem is reduced to the one of computing planar arrangements of algebraic curves. We succeed in locating all event points in these arrangements, including tangential intersections and singular points. By introducing an additional curve, which we call the Jacobi curve, we are able to find non-singular tangential intersections. We show that the coordinates of the singular points in our special projected plana…

Discrete mathematicsPure mathematicsArrangementsControl and OptimizationFunction field of an algebraic varietyAlgebraic curvesMathematicsofComputing_NUMERICALANALYSISComputational geometryComputer Science ApplicationsComputational MathematicsComputational Theory and MathematicsJacobian curveAlgebraic surfaceComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONReal algebraic geometryAlgebraic surfacesExact algebraic computationAlgebraic functionGeometry and TopologyAlgebraic curveAlgebraic numberRobustnessMathematicsSingular point of an algebraic varietyComputational Geometry
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Periodic Spline Wavelets and Wavelet Packets

2014

This chapter presents wavelets and wavelet packets in the spaces of periodic splines of arbitrary order, which, in essence, are the multiple generators for these spaces. The SHA technique provides explicit representation of the wavelets and wavelet packets and fast implementation of the transforms in one and several dimensions.

Discrete wavelet transformSpline (mathematics)WaveletLifting schemeLegendre waveletComputer scienceGabor waveletComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONMathematicsofComputing_NUMERICALANALYSISOrthonormal basisData_CODINGANDINFORMATIONTHEORYAlgorithmWavelet packet decomposition
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Improved color interpolation using discrete wavelet transform

2005

New approaches to Color Interpolation based on Discrete Wavelet Transform are described. The Bayer data are split into the three colour components; for each component the Wavelet Coefficient Interpolation (WCI) algorithm is applied and results are combined to obtain the final colour interpolated image. A further anti-aliasing algorithm can be applied in order to reduce false colours. A first approach consists of interpolating wavelet coefficients starting from a spatial analysis of the input image. It was considered an interpolation step based on threshold levels associated to the spatial correlation of the input image pixel. A second approach consists of interpolating wavelet coefficients …

Discrete wavelet transformWaveletLifting schemeSecond-generation wavelet transformStationary wavelet transformMathematicsofComputing_NUMERICALANALYSISComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONWavelet transformHarmonic wavelet transformAlgorithmWavelet packet decompositionMathematics
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Potential implementation of reservoir computing models based on magnetic skyrmions

2018

Reservoir Computing is a type of recursive neural network commonly used for recognizing and predicting spatio-temporal events relying on a complex hierarchy of nested feedback loops to generate a memory functionality. The Reservoir Computing paradigm does not require any knowledge of the reservoir topology or node weights for training purposes and can therefore utilize naturally existing networks formed by a wide variety of physical processes. Most efforts prior to this have focused on utilizing memristor techniques to implement recursive neural networks. This paper examines the potential of skyrmion fabrics formed in magnets with broken inversion symmetry that may provide an attractive phy…

Distributed computingMathematicsofComputing_NUMERICALANALYSISFOS: Physical sciencesGeneral Physics and Astronomy02 engineering and technologyMemristor01 natural scienceslaw.inventionlawMesoscale and Nanoscale Physics (cond-mat.mes-hall)0103 physical sciences010306 general physicsTopology (chemistry)PhysicsCondensed Matter - Mesoscale and Nanoscale PhysicsArtificial neural networkHierarchy (mathematics)SkyrmionReservoir computingPhysik (inkl. Astronomie)021001 nanoscience & nanotechnologylcsh:QC1-999Recurrent neural networkNode (circuits)0210 nano-technologylcsh:PhysicsAIP Advances
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On Fuzzy Stochastic Integral Equations—A Martingale Problem Approach

2011

In the paper we consider fuzzy stochastic integral equations using the methods of stochastic inclusions. The idea is to consider an associated martingale problem and its solutions in order to obtain a solution to the fuzzy stochastic equation.

Doob's martingale inequalityStratonovich integralMathematical optimizationContinuous-time stochastic processComputingMethodologies_SIMULATIONANDMODELINGMathematicsofComputing_NUMERICALANALYSISLocal martingaleMartingale difference sequenceStochastic optimizationMartingale (probability theory)Fuzzy logicMathematics
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