Search results for "Conjugate gradient method"

showing 3 items of 23 documents

CALIBRATION OF LÉVY PROCESSES USING OPTIMAL CONTROL OF KOLMOGOROV EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS

2018

We present an optimal control approach to the problem of model calibration for L\'evy processes based on a non parametric estimation procedure. The calibration problem is of considerable interest in mathematical finance and beyond. Calibration of L\'evy processes is particularly challenging as the jump distribution is given by an arbitrary L\'evy measure, which form a infinite dimensional space. In this work, we follow an approach which is related to the maximum likelihood theory of sieves. The sampling of the L\'evy process is modelled as independent observations of the stochastic process at some terminal time $T$. We use a generic spline discretization of the L\'evy jump measure and selec…

non-parametric maximum likelihood methodOptimization problemDiscretizationL ́evy processesoptimal control of PIDE010103 numerical & computational mathematics01 natural sciences93E10 (primary) 49K20 60G51 62G05 (secondary)010104 statistics & probabilitysymbols.namesakeConjugate gradient methodIMEX numerical methodQA1-939Applied mathematics0101 mathematicsMathematics - Optimization and ControlMathematicsKolmogorov-Fokker-Planck equationoptimal control of PIDE Kolmogorov-Fokker-Planck equation L ́evy processes non-parametric maximum likelihood method IMEX numerical method.SolverOptimal controlSpline (mathematics)Lévy processesModeling and SimulationLagrange multipliersymbolsAkaike information criterionMathematicsAnalysisMathematical Modelling and Analysis
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A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

2015

Variational methods are commonly used to solve noise removal problems. In this paper, we present an augmented Lagrangian-based approach that uses a discrete form of the L1-norm of the mean curvature of the graph of the image as a regularizer, discretization being achieved via a finite element method. When a particular alternating direction method of multipliers is applied to the solution of the resulting saddle-point problem, this solution reduces to an iterative sequential solution of four subproblems. These subproblems are solved using Newton’s method, the conjugate gradient method, and a partial solution variant of the cyclic reduction method. The approach considered here differs from ex…

ta113Mean curvatureDiscretizationimage denoisingAugmented Lagrangian methodApplied MathematicsGeneral Mathematicsmean curvaturekuvankäsittelyTopologyFinite element methodimage processingsymbols.namesakeLagrangian relaxationLagrange multiplierConjugate gradient methodsymbolsApplied mathematicsaugmented Lagrangian methodalternating direction methods of multipliersvariational modelMathematicsCyclic reductionSIAM Journal on Imaging Sciences
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Evaluating the performance of artificial neural networks for the classification of freshwater benthic macroinvertebrates

2014

Abstract Macroinvertebrates form an important functional component of aquatic ecosystems. Their ability to indicate various types of anthropogenic stressors is widely recognized which has made them an integral component of freshwater biomonitoring. The use of macroinvertebrates in biomonitoring is dependent on manual taxa identification which is currently a time-consuming and cost-intensive process conducted by highly trained taxonomical experts. Automated taxa identification of macroinvertebrates is a relatively recent research development. Previous studies have displayed great potential for solutions to this demanding data mining application. In this research we have a collection of 1350 …

ta113Radial basis function networkEcologyArtificial neural networkComputer sciencebusiness.industryApplied MathematicsEcological Modelingta1172PerceptronMachine learningcomputer.software_genreBackpropagationComputer Science ApplicationsProbabilistic neural networkIdentification (information)Computational Theory and MathematicsModeling and SimulationMultilayer perceptronConjugate gradient methodta1181Artificial intelligencebusinesscomputerEcology Evolution Behavior and SystematicsEcological Informatics
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