The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sw...The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sweeping method are presented. These parallel algorithms are simple and efficient due to the causality of the underlying partial different equations. Numerical examples are used to verify our algorithms.展开更多
针对传统的混合表面形状恢复算法存在较大误差的问题,提出了一种基于透视投影的从混合表面的明暗变化恢复形状的新算法。首先,建立了一种改进的Ward反射模型来描述混合表面的反射特性,其次,采用更接近摄像机实际拍摄的透视投影方式,并...针对传统的混合表面形状恢复算法存在较大误差的问题,提出了一种基于透视投影的从混合表面的明暗变化恢复形状的新算法。首先,建立了一种改进的Ward反射模型来描述混合表面的反射特性,其次,采用更接近摄像机实际拍摄的透视投影方式,并且假定光源位于摄像机的光心处,构造了新模型下的图像辐照度方程,然后将该方程转化为包含物体表面深度信息的Hamilton-Jacobi偏微分方程,使用Fixed-point Iterative Sweeping方法和2D Central Hamiltonian函数逼近该微分方程的黏性解,进而得到物体表面的三维形状。与同类算法相比,新算法恢复的结果更加准确有效。合成花瓶图像的实验结果表明,与基于正交投影的算法相比,新算法恢复三维形状高度的平均误差和均方根误差均有较大幅度减少。展开更多
The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a u...The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation.展开更多
In this paper, we study the viscosity solutions of the Neumann problem in a bounded C<sup>2</sup> domain Ω, where Δ<sup>N</sup>∞</sub> is called the normalized infinity Laplacian. The ...In this paper, we study the viscosity solutions of the Neumann problem in a bounded C<sup>2</sup> domain Ω, where Δ<sup>N</sup>∞</sub> is called the normalized infinity Laplacian. The normalized infinity Laplacian was first studied by Peres, Shramm, Sheffield and Wilson from the point of randomized theory named tug-of-war, which has wide applications in optimal mass transportation, financial option price problems, digital image processing, physical engineering, etc. We give the Lipschitz regularity of the viscosity solutions of the Neumann problem. The method we adopt is to choose suitable auxiliary functions as barrier functions and combine the perturbation method and viscosity solutions theory. .展开更多
This paper concerns the weak solutions of some Monge-Amp^re type equa- tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Ampere typ...This paper concerns the weak solutions of some Monge-Amp^re type equa- tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Ampere type equations is discussed. A uniform estimate for solution of the Dirichlet problem with homogeneous boundary value is obtained.展开更多
In this paper, we first give a comparison theorem of viscosity solution to some nonlinear second order integrodifferential equation. And then using the comparison theorem, we obtain a necessary and sufficient conditio...In this paper, we first give a comparison theorem of viscosity solution to some nonlinear second order integrodifferential equation. And then using the comparison theorem, we obtain a necessary and sufficient condition for the viability property of some controlled jump diffusion processes which can keep the solution within a constraint K.展开更多
基金This work is partially supported by Sloan FoundationNSF DMS0513073+1 种基金ONR grant N00014-02-1-0090DARPA grant N00014-02-1-0603
文摘The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sweeping method are presented. These parallel algorithms are simple and efficient due to the causality of the underlying partial different equations. Numerical examples are used to verify our algorithms.
文摘针对传统的混合表面形状恢复算法存在较大误差的问题,提出了一种基于透视投影的从混合表面的明暗变化恢复形状的新算法。首先,建立了一种改进的Ward反射模型来描述混合表面的反射特性,其次,采用更接近摄像机实际拍摄的透视投影方式,并且假定光源位于摄像机的光心处,构造了新模型下的图像辐照度方程,然后将该方程转化为包含物体表面深度信息的Hamilton-Jacobi偏微分方程,使用Fixed-point Iterative Sweeping方法和2D Central Hamiltonian函数逼近该微分方程的黏性解,进而得到物体表面的三维形状。与同类算法相比,新算法恢复的结果更加准确有效。合成花瓶图像的实验结果表明,与基于正交投影的算法相比,新算法恢复三维形状高度的平均误差和均方根误差均有较大幅度减少。
文摘The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation.
文摘In this paper, we study the viscosity solutions of the Neumann problem in a bounded C<sup>2</sup> domain Ω, where Δ<sup>N</sup>∞</sub> is called the normalized infinity Laplacian. The normalized infinity Laplacian was first studied by Peres, Shramm, Sheffield and Wilson from the point of randomized theory named tug-of-war, which has wide applications in optimal mass transportation, financial option price problems, digital image processing, physical engineering, etc. We give the Lipschitz regularity of the viscosity solutions of the Neumann problem. The method we adopt is to choose suitable auxiliary functions as barrier functions and combine the perturbation method and viscosity solutions theory. .
基金supported by National Natural Science Foundation of China(11071119)
文摘This paper concerns the weak solutions of some Monge-Amp^re type equa- tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Ampere type equations is discussed. A uniform estimate for solution of the Dirichlet problem with homogeneous boundary value is obtained.
基金the National Basic Research Program of China (973 Program) Grant No.2007CB814900 (Financial Risk)
文摘In this paper, we first give a comparison theorem of viscosity solution to some nonlinear second order integrodifferential equation. And then using the comparison theorem, we obtain a necessary and sufficient condition for the viability property of some controlled jump diffusion processes which can keep the solution within a constraint K.
