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Two anisotropic fourth-order partial differential equations for image inpainting

IET IMAGE PROCESSING 2013年第3期7卷 260-269页

作者： Li, Peng Li, Shuai-Jie Yao, Zheng-An Zhang, Zu-Jin Sun Yat Sen Univ Sch Math & Computat Sci Guangzhou 510275 Guangdong Peoples R China Henan Univ Sci & Technol Sch Math & Stat Luoyang 471003 Peoples R China Gannan Normal Univ Coll Math & Comp Sci Ganzhou 341000 Peoples R China

In this study, the authors propose two fourth-order partial differential equations (PDEs) to inpaint the image. By analysing those anisotropic fourth-order PDEs and comparing their diffusion images, the authors confirm they are forward diffusion or backward diffusion. A numerical algorithm is presented using a finite-difference method and analyse the stability of discretisation. Finally, they show various experimental results and conclude that the proposed new models are better than the second-order and third-order PDEs, especially for weakening the blocky effects.

关键词： finite difference methods image texture numerical stability partial differential equations anisotropic fourth-order partial differential equations image inpainting anisotropic fourth-order PDE diffusion images forward diffusion backward diffusion numerical algorithm finite-difference method stability discretisation second-order PDE third-order PDE blocky effects finite difference methods image texture numerical stability partial differential equations anisotropic fourth-order partial differential equations image inpainting anisotropic fourth-order PDE diffusion images forward diffusion backward diffusion numerical algorithm finite-difference method stability discretisation second-order PDE third-order PDE blocky effects

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numerical method and convergence order for second-order impulsive differential equations

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ADVANCES IN DIFFERENCE EQUATIONS 2019年第1期2019卷 260-260页

作者： Mei, Liangcai Sun, Hongbo Lin, Yingzhen Beijing Inst Technol Zhuhai Campus Zhuhai Peoples R China

This paper is devoted to the numerical scheme for the impulsive differential equations. The main idea of this method is, for the first time, to establish a broken reproducing kernel space that can be used in pulse models. Then the uniform convergence of the numerical solution is proved, and the time consuming Schmidt orthogonalization process is avoided. The proposed method is proved to be stable and have the second-order convergence. The algorithm is proved to be feasible and effective through some numerical examples.

关键词： Impulsive differential equations Broken reproducing kernel space Convergence order numerical algorithm

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A class of portfolio selection with a four-factor futures price model

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ANNALS OF OPERATIONS RESEARCH 2008年第1期164卷 139-165页

作者： Yan, Wei Li, Shurong Chinese Acad Sci Inst Syst Sci Acad Math & Syst Sci Beijing 100080 Peoples R China China Univ Petr Coll Informat & Control Engn Dongying Shandong 257061 Peoples R China

Considering the stochastic exchange rate, a four-factor futures model with the underling asset, convenience yield, instantaneous risk free interest rate and exchange rate, is established. These processes follow jump-diffusion processes (Weiner process and Poisson process). The corresponding partial differential equation (PDE) of the futures price is derived. The general solution of the PDE with parameters is drawn. The weight least squares approach is applied to obtain the parameters of above PDE. Variance is substituted by semi-variance in Markowitzs portfolio selection model. Therefore, a class of multi-period semi-variance model is formulated originally. Then, a continuous-time mean-variance portfolio model is also considered. The corresponding stochastic Hamilton-Jacobi-Bellman (HJB) equation of the problem with nonlinear constraints is derived. A numerical algorithm is proposed for finding the optimal solution in this paper. Finally, in order to demonstrate the effectiveness of the theoretical models and numerical methods, the fuel futures in Shanghai exchange market and the Brent crude oil futures in London exchange market are selected to be examples.

关键词： Four-factor model Multi-period semi-variance portfolio Exchange rate Futures numerical algorithm

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State Estimation by Continuous-Time Observations in Multiplicative Noise

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IFAC-PapersOnLine 2017年第1期50卷 1601-1606页

作者： Borisov A.V. Semenikhin K.V. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences Moscow Russian Federation Moscow Aviation Institute (National Research University) Moscow Russian Federation

The paper is devoted to the Bayesian estimation of finite-state random vector given the indirect non-stationary continuous-time observations corrupted by a Wiener noise. The key feature is that the noise intensity is a function of the estimated vector, hence the traditional optimal filtering framework fails in this case. The estimate is obtained both in the explicit integral form and as the solution to a stochastic Differential system with some jump processes in the right hand side. The presence of the multiplicative noise gives a possibility to raise the estimation quality up to the exact value restoration. The numerical procedure for the estimate calculation is accompanied with the accuracy analysis. An example illustrating the performance of the proposed estimate is also presented. © 2017

关键词： continuous time filter local smoothing multiplicative noise numerical algorithm Optimal estimation

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Navigation in non-inertial terrestrial frames using the attitude matrices

Navigation in non-inertial terrestrial frames using the atti...

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48th International Symposium ELMAR-2006 on Multimedia Signal Processing and Communications

作者： Grigorie, Teodor Lucian Sandu, Dragos George Aron, Ioan Univ Craiova Fac Elect Engn Craiova Romania Flight Test Ctr Craiova Romania Univ Politehn Bucuresti Fac Aerosp Engn Bucharest Romania

ISBN: (纸本)9789537044039

The paper presents a numerical algorithm used to establish the position of a vehicle reported to the Earth s geographical frame. The method we suggest based on the direct integration of the equation of inertial navigation, considering the vehicle's attitude as a result of the integration of the differential matriceal attitude equation. This integration is performed using a quick method, the induced commutation error being avoided with a numerical logistics which implies the usage of the data acquisition card from strop-down gyrometers in the navigation processor

关键词： inertial navigation strap-down systems attitude matrices numerical algorithm

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Un algoritmo iterativo para la estimacion de modelos arma con ausencia de observaciones

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Trabajos de Estadistica 1988年第2期3卷 141-156页

作者： Cristóbal, A.Cristóbal Dpto. de Métodos Estadisticos Universidad de Zaragoza Zaragoza Spain

In this paper, an iterative algorithm to estimate para meters of ARMA models with missing observations is given. Furthermore, the convergence of the algorithm is proved. A example based in simulation of time series wi... 详细信息

关键词： 62M10 65U05 estimation numerical algorithm time series

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Simulation and Analysis of Coupled Vibration of Monorail Train-bridge-road Vehicle System 5

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5th International Symposium on Environmental Vibration (ISEV2011)

作者： Chen, Shangyou Liu, Gao Xia, He Lu, Ping CCCC Highway Consultants CO Ltd Beijing 100088 Peoples R China Beijing Jiaotong Univ Sch Civil Engn Beijing 100044 Peoples R China CCCC Water Transportat Consultants CO Ltd Beijing 100007 Peoples R China

ISBN: (纸本)9787030323736

A space dynamic analysis model of monorail train-bridge-vehicle coupled vibration system is established,in which the monorail train and road vehicles are idealized as the combination of a number of rigid bodies connected by a series of springs and dampers. The degree-of-freedom(DOF) of a car in monorail train is 15,and that of a road vehicle is 13 for 2-axle car or 17 for 3-axle car. Bridges are considered as an assemblage of beam elements with 6 DOFs at each node and link elements with 3 DOFs at each node. The contact between the bridge and the moving vehicle and train is assumed to be a point contact. Based on the displacement corresponding relationship of bridge and vehicle,the equations of motion of the coupled monorail train-bridge-road vehicle system are introduced. A numerical algorithm is then proposed for solving the nonlinear dynamic equations of the coupled system. A corresponding computer code is developed to get the dynamic response of the full bridge and trains and vehicles. With an actual bridge as an example, the dynamic responses of the bridge and riding comfort indexes of the trains and the vehicles are evaluated. The results show that the bridge is safety,and the proposed analysis model and the solution method are feasible.

关键词： monorail train train-bridge-vehicle system coupled vibration numerical algorithm dynamic responses

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Conditional Multidimensional Parameter Identification with Asymmetric Correlated Losses of Estimation Errors 21

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21st International Conference on Neural Information Processing (ICONIP)

作者： Kulczycki, Piotr Charytanowicz, Malgorzata Polish Acad Sci Syst Res Inst Warsaw Poland John Paul II Catholic Univ Lublin Lublin Poland

ISBN: (纸本)9783319126401

This paper is dedicated to the problem of the estimation of a vector of parameters, as losses resulting from their under- and overestimation are asymmetric and mutually correlated. The issue is considered from an additional conditional aspect, where particular coordinates of conditioning variables may be continuous, binary, discrete or categorized (ordered and unordered). The final result is an algorithm for calculating the value of an estimator, optimal in sense of expectation of losses using a multidimensional asymmetric quadratic function, for practically any distributions of describing and conditioning variables.

关键词： parameters' vector identification conditional factors Bayes approach asymmetric loss function distribution free method numerical algorithm

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On Convergence of Higher Order Differential-Difference Schemes for Telegraph Equation

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VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS 2024年第4期57卷 499-513页

作者： Hieu, Le Minh Xuan, Nguyen Huu Nguyen Univ Danang Univ Econ Fac Econ Da Nang 590000 Vietnam Univ Danang Univ Econ Dept Res & Int Cooperat Da Nang 590000 Vietnam

The purpose of this article is to introduce an approximation method for solving the Dirichlet initial boundary value problem (IBVP) for the telegraph equation. The approach involves the idea of discretizing a spatial variable and utilizing the integral-interpolation method with specific fundamental functions. The original equation is multiplied by auxiliary functions, and subsequently interpolation and integration methods are applying on the spatial variable to generate system of ordinary differential equations (ODEs). Flexible applications of the Newton-Stirling and Hermite-Birkhoff interpolations are made to internal and close-to-boundary nodes. Additionally, the boundary conditions are automatically satisfied without the need for a separate approximation as in classical numerical methods like the grid method or the method of lines. As a result, the suggested schemes have a higher level of approximation. To prove the convergence of differential-difference schemes of high degree of accuracy, the logarithmic norm of the matrix is used.

关键词： telegraph equation partial differential equation (PDE) numerical solution numerical algorithm differential-difference scheme Hermite-Birkhoff interpolation Newton-Stirling interpolation logarithmic norm integral-interpolation method

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SiMpLIfy: A Toolbox for Structured Model Reduction

SiMpLIfy: A Toolbox for Structured Model Reduction

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European Control Conference (ECC)

作者： Biel, Martin Farokhi, Farhad Sandberg, Henrik KTH Royal Inst Technol ACCESS Linnaeus Ctr Sch Elect Engn SE-10044 Stockholm Sweden Univ Melbourne Dept Elect & Elect Engn Parkville Vic 3010 Australia

ISBN: (纸本)9783952426937

In this paper, we present a toolbox for structured model reduction developed for MATLAB. In addition to structured model reduction methods using balanced realizations of the subsystems, we introduce a numerical algorithm for structured model reduction using a subgradient optimization algorithm. We briefly present the syntax for the toolbox and its features. Finally, we demonstrate the applicability of various model reduction methods in the toolbox on a structured mass-spring mechanical system.

关键词： gradient methods numerical analysis optimisation reduced order systems MATLAB SiMpLIfy balanced realization numerical algorithm structured mass-spring mechanical system structured model reduction method subgradient optimization algorithm toolbox Controllability Interconnected systems Observability Optimization Periodic structures Reduced order systems Transfer functions

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