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Convergence Estimates for Some regularization methods to Solve a Cauchy Problem of the Laplace Equation

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Numerical Mathematics(Theory,methods and Applications) 2011年第4期4卷 459-477页

作者： T.Wei H.H.Qin H.W.Zhang School of Mathematics and Statistics Lanzhou UniversityP.R.China

In this paper,we give a general proof on convergence estimates for some regularization methods to solve a Cauchy problem for the Laplace equation in a rectangular *** regularization methods we considered are:a non-local boundary value problem method,a boundary Tikhonov regularization method and a generalized *** on the conditional stability estimates,the convergence estimates for various regularization methods are easily obtained under the simple verifications of some *** results for one example show that the proposed numerical methods are effective and stable.

关键词： Cauchy problem Laplace equation regularization methods convergence estimates

Measurement of nonuniform temperature distribution by combining line-of-sight TDLAS with regularization methods

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Instrumentation 2014年第3期1卷 43-57页

作者： LIU Chang XU Lijun CAO Zhang Ministry of Education's Key Laboratory of Precision Opto-mechatronics Technology School of Instrumentation and Opto-Electronic EngineeringBeihang UniversityBeijing 100191China

regularization methods were combined with line-of-sight tunable diode laser absorption spectroscopy(TDLAS)to measure nonuniform temperature *** on measurements of 12 absorption transitions of water vapor from 1300 nm to 1350 nm,the temperature probability distribution of nonuniform temperature distribution,for which a parabolic temperature profile is selected as an example in this paper,was retrieved by making the use of regularization *** examine the effectiveness of regularization methods,truncated singular value decomposition(TSVD),Tikhonov regularization and a revised Tikhonov regularization method were implemented to retrieve the temperature probability *** results derived by using the three regularization methods were compared with that by using constrained linear least-square *** results show that regularization methods not only generate closer temperature probability distributions to the original,but also are less sensitive to measurement ***,the revised Tikhonov regularization method generate solutions in better agreement with the original ones than those obtained by using TSVD and Tikhonov regularization *** results obtained in this work can enrich the temperature distribution information,which is expected to play a more important role in combustion diagnosis.

关键词： tunable diode laser absorption spectroscopy(TDLAS) temperature ine-of-sight measurement regularization methods

THEORETICAL ANALYSES AND NUMERICAL EXPERIMENTS FOR TWO-DIMENSIONAL WIND RETRIEVALS FROM SINGLE-DOPPLER DATA

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Journal of Hydrodynamics 2010年第2期22卷 185-195页

作者： HUANG Si-xun CAO Xiao-qun DU Hua-dong ZHONG Ji-qin Institute of Meteorology PLA University of Science and Technology Nanjing 211101 China National University of Defense Technolog Changsha 410073 China Institute of Urban Meteorology China Meteorological Administration Beijing 100089 China

Based on variational adjoint methods,theoretical analyses and numerical experiments are performed for retrievals of two-dimensional winds and related parameters from single-Doppler radar data in polar *** the method,the reflectivity conservation equation is used as the governing equation and the mass continuity equation as a weak *** the same time,the stable functional of regularization and background field are also introduced in the cost *** on the ideal experiments with artificial data,real two-dimensional wind fields are retrieved with low-altitude data from the Nanjing Doppler Radar Station,and the results are encouraging and promising.

关键词： single-Doppler retrievals adjoint methods regularization methods two-dimensional wind

On the Numerical Solution of Some Eikonal Equations:An Elliptic Solver Approach

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Chinese Annals of Mathematics,Series B 2015年第5期36卷 689-702页

作者： Alexandre CABOUSSAT Roland GLOWINSKI Tsorng-Whay PAN Haute Ecole de Gestion de Genève University of Applied Sciences Department of Mathematics University of Houston

The steady Eikonal equation is a prototypical first-order fully nonlinear equation. A numerical method based on elliptic solvers is presented here to solve two different kinds of steady Eikonal equations and compute solutions, which are maximal and minimal in the variational sense. The approach in this paper relies on a variational argument involving penalty, a biharmonic regularization, and an operator-splitting-based time-discretization scheme for the solution of an associated initial-value problem. This approach allows the decoupling of the nonlinearities and differential *** experiments are performed to validate this approach and investigate its convergence properties from a numerical viewpoint.

关键词： Eikonal equations Maximal solutions regularization methods Operator slalitting Finite element methods

H→γγ:a comment on the indeterminacy of non-gauge-invariant integrals

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Chinese Physics C 2013年第4期37卷 7-13页

作者： F.Piccinini A.Pilloni A.D.Polosa INFN Pavia-Via A.Bassi 6 I-27100PaviaItaly Dipartimento di Fisica and INFN 'Sapienza' Università di Roma-P.le A.Moro 2I-00185RomaItaly

We reanalyze the recent computation of the amplitude of the Higgs boson decay into two photons presented by Gastmans et al. [1, 2]. The reasons for why this result cannot be the correct one have been discussed in some recent papers. We address here the general issue of the indeterminacy of integrals with four-dimensional gauge-breaking regulators and to which extent it might eventually be solved by imposing physical constraints. Imposing gauge invariance as the last step upon Rξ-gauge calculations with four-dimensional gauge-breaking regulators, allows us to recover the well known H→γγ result. However we show that in the particular case of the unitary gauge, the indeterminacy cannot be tackled in the same way. The combination of the unitary gauge with a cutoff regularization scheme turns out to be non-predictive.

关键词： Higgs decay regularization methods loop calculations gauge invariance

GENERALIZED VARIATIONAL OPTI MAZATION ANALYSIS FOR2-D FLOW FIELD

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Journal of Hydrodynamics 2005年第4期17卷 459-465页

作者： HUANG Si-xun XU Ding-hua LAN Wei-ren TENG Jia-jun Institute of Meteorology PLA University of Science and Technology Nanjing 211101 China LMSWE Nanjing University Nanjing 210093 China LMSWE Nanjing University Nanjing 210093 China East China Technology Institute Fuzhou 344000 China Institute of Meteorology PLA University of Science and Technology Nanjing 211101 China

The Variational Optimization Analysis Method （VOAM） for 2-D flow field suggested by Sasaki was reviewed first. It is known that the VOAM can he used efficiently in most cases. However, in the cases where there are high frequency noises in 2-D flow field, it appears to be inefficient. In the present paper, based on Sasaki＇s VOAM, a Generalized Variational Optimization Analysis Method （GVOAM） was proposed with regularization ideas, which could deal well with flow fields containing high frequency noises. A numerical test shows that observational data can be both variationally optimized and filtered, and therefore the GVOAM is an efficient method.

关键词： variational optimization analysis regularization methods generalized variational optimization analysis

Generalized Method of Variational Analysis for 3-D Flow

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Advances in Atmospheric Sciences 2004年第5期21卷 730-740页

作者：兰伟仁黄思训项杰 Meteorological College PLA University of Science and TechnologyNanjing 211101

The generalized method of variational analysis (GMVA) suggested for 2-D wind observations by Huang et al. is extended to 3-D cases. Just as in 2-D cases, the regularization idea is applied. But due to the complexity of the 3-D cases, the vertical vorticity is taken as a stable functional. The results indicate that wind observations can be both variationally optimized and ?ltered. The e?ciency of GMVA is also checked in a numerical test. Finally, 3-D wind observations with random disturbances are manipulated by GMVA after being ?ltered.

关键词： regularization methods inverse problem generalized method of variational analysis ?lter- ing

A Penalty-regularization-Operator Splitting Method for the Numerical Solution of a Scalar Eikonal Equation

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Chinese Annals of Mathematics,Series B 2015年第5期36卷 659-688页

作者： Alexandre CABOUSSAT Roland GLOWINSKI Haute Ecole de Gestion de Genève HES-SO//University of Applied Sciences Department of Mathematics University of Houston

In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.

关键词： Eikonal equation Minimal and maximal solutions regularization methods Penalization of equality constraints Dynamical flow Operator splitting Finite element methods

A primer on stable parameter estimation and forecasting in epidemiology by a problem-oriented regularized least squares algorithm

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Infectious Disease Modelling 2017年第2期2卷 268-275页

作者： Alexandra Smirnova Gerardo Chowell Department of Mathematics and Statistics Georgia State UniversityAtlantaUSA School of Public Health Georgia State UniversityAtlantaUSA Division of International Epidemiology and Population Studies Fogarty International CenterNational Institutes of HealthBethesdaMDUSA

Public health officials are increasingly recognizing the need to develop disease-forecasting systems to respond to epidemic and pandemic *** instance,simple epidemic models relying on a small number of parameters can play an important role in characterizing epidemic growth and generating short-term epidemic *** the absence of reliable information about transmission mechanisms of emerging infectious diseases,phenomenological models are useful to characterize epidemic growth patterns without the need to explicitly model transmission mechanisms and the natural history of the *** this article,our goal is to discuss and illustrate the role of regularization methods for estimating parameters and generating disease forecasts using the generalized Richards model in the context of the 2014e15 Ebola epidemic in West Africa.

关键词： Generalized Richards model Parameter estimation regularization methods Epidemic forecasting Ebola