NUMERICAL RECONSTRUCTION OF SMALL PERTURBATIONS IN THE ELECTROMAGNETIC COEFFICIENTS OF A DIELECTRIC MATERIAL

The aim of this paper is to solve numerically the inverse problem of reconstructing small amplitude perturbations in the magnetic permeability of a dielectric material from partial or total dynamic boundary measurements. Our numerical algorithm is based on the resolution of the time-dependent Maxwell equations, an exact controllability method and Fourier inversion for localizing the perturbations. Two-dimensional numerical experiments illustrate the performance of the reconstruction method for different configurations even in the case of limited-view data.     

ON REMES ALGORITHA FOR THE BEST CHEBYSHEV APPROXIMATION FROM VARISOLVENT FAMILY

In this paper, Remes algorithm is applied to compute the numerical solution of the best chebyshev approximation from varisolvent family. Feasibility and convergence of the algorithm are discussed carefully.     

ON THE GLOBAL ALGORITHM FOR FINDING ZEROS OF GENERAL MAPPINGS OVER R~2

This paper presents a simplicial method for numerically approximating all zeros of a generic mapping over. R by use of the complex degree proposed by the authors . The detail of an algorithm, which can be implemented easily, is outlined sufficiently. Some numerical examples are given for further illustrating the convergence and the stability of the algorithm.     

A QR DECOMPOSITION BASED SOLVER FOR THE LEAST SQUARES PROBLEMS FROM THE MINIMAL RESIDUAL METHOD FOR THE SYLVESTER EQUATION

Based on the generalized minimal residual （GMRES） principle, Hu and Reichel proposed a minimal residual algorithm for the Sylvester equation. The algorithm requires the solution of a structured least squares problem. They form the normal equations of the least squares problem and then solve it by a direct solver, so it is susceptible to instability. In this paper, by exploiting the special structure of the least squares problem and working on the problem directly, a numerically stable QR decomposition based algorithm is presented for the problem. The new algorithm is more stable than the normal equations algorithm of Hu and Reichel. Numerical experiments are reported to confirm the superior stability of the new algorithm.     

Positivity and boundedness preserving schemes for the fractional reaction-difusion equation

In this paper,we design a semi-implicit scheme for the scalar time fractional reaction-difusion equation.We theoretically prove that the numerical scheme is stable without the restriction on the ratio of the time and space stepsizes,and numerically show that the convergence orders are 1 in time and 2 in space.As a concrete model,the subdifusive predator-prey system is discussed in detail.First,we prove that the analytical solution to the system is positive and bounded.Then,we use the provided numerical scheme to solve the subdifusive predator-prey system,and theoretically prove and numerically verify that the numerical scheme preserves the positivity and boundedness.     

一类非线性互补问题的信赖域算法

In this paper,an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed.A feature of this algorithm is that only the solution of linear systems of equations is required at each iteration,thus avoiding the need for solving a quadratic subproblem with a trust region bound.Under some conditions,it is proven that this algorithm is globally and locally superlinear convergent.The limited numerical examples show its efficiency.     

Joint optimization traffic signal control for an urban arterial road

This paper considers the optimal traffic signal setting for an urban arterial road. By introducing the concepts of synchronization rate and non-synchronization degree, a mathematical model is constructed and an optimization problem is posed. Then, a new iterative algorithm is developed to solve this optimal traffic control signal setting problem. Convergence properties for this iterative algorithm are established. Finally, a numerical example is solved to illustrate the effectiveness of the method.     

A NATURAL GRADIENT ALGORITHM FOR THE SOLUTION OF LYAPUNOV EQUATIONS BASED ON THE GEODESIC DISTANCE

A new framework based on the curved Riemannian manifold is proposed to calculate the numerical solution of the Lyapunov matrix equation by using a natural gradient descent algorithm and taking the geodesic distance as the objective function. Moreover, a gradient descent algorithm based on the classical Euclidean distance is provided to compare with this natural gradient descent algorithm. Furthermore, the behaviors of two proposed algorithms and the conventional modified conjugate gradient algorithm are compared and demonstrated by two simulation examples. By comparison, it is shown that the convergence speed of the natural gradient descent algorithm is faster than both of the gradient descent algorithm and the conventional modified conjugate gradient algorithm in solving the Lyapunov equation.     

Crank-Nicolson拟合有限体积法定价机制转换下的欧式期权

This paper develops and analyses a novel numerical scheme to price European options under regime switching model which is governed by a system of partial differential equations(PDEs).To numerically solve these PDEs,we introduce a fitted finite volume method for the spatial discretization,coupled with the Crank-Nicolson time stepping scheme.We show that this scheme is consistent,stable and monotone,and hence the convergence of the numerical solution to the viscosity solution of the continuous problem is guaranteed.Numerical experiments are presented to demonstrate the accuracy,efficiency and robustness of the new numerical method.     

A Novel Genetic Algorithm for Global Optimization

This paper presents a novel genetic algorithm for globally solving un-constraint optimization problem.In this algorithm,a new real coded crossover operator is proposed firstly.Furthermore,for improving the convergence speed and the searching ability of our algorithm,the good point set theory rather than random selection is used to generate the initial population,and the chaotic search operator is adopted in the best solution of the current iteration.The experimental results tested on numerical benchmark functions show that this algorithm has excellent solution quality and convergence characteristics,and performs better than some algorithms.     

Smooth factorizations of matrix valued functions and their derivatives

Summary In this paper we study the numerical factorization of matrix valued functions in order to apply them in the numerical solution of differential algebraic equations with time varying coefficients. The main difficulty is to obtain smoothness of the factors and a numerically accessible form of their derivatives. We show how this can be achieved without numerical differentiation if the derivative of the given matrix valued function is known. These results are then applied in the numerical solution of differential algebraic Riccati equations. For this a numerical algorithm is given and its properties are demonstrated by a numerical example.     

Numerical Solution of Riemann–Hilbert Problems: Random Matrix Theory and Orthogonal Polynomials

Recently, a general approach to solving Riemann–Hilbert problems numerically has been developed. We review this numerical framework and apply it to the calculation of orthogonal polynomials on the real line. Combining this numerical algorithm with the approach of Bornemann to compute Fredholm determinants, we are able to calculate spectral densities and gap statistics for a broad class of finite-dimensional unitary invariant ensembles. We show that the accuracy of the numerical algorithm for approximating orthogonal polynomials is uniform as the degree grows, extending the existing theory to handle g-functions. As another example, we compute the Hastings–McLeod solution of the homogeneous Painlevé II equation.     

Convergence of a parameter switching algorithm for a class of nonlinear continuous systems and a generalization of Parrondo’s paradox

In this paper, we prove the convergence of a numerical algorithm that switches in some deterministic or random manner, the control parameter of a class of continuous-time nonlinear systems while the underlying initial value problem is numerically integrated. The numerically obtained attractor is a good approximation of the attractor obtained when the control parameter is replaced with the average of the switched values. In this way, a generalization of Parrondo’s paradox can be obtained. As an application, the Lorenz and Rabinovich–Fabrikant systems are used for illustration.     

Homotopy perturbation method for (2+1) -dimensional coupled Burgers system

In this paper, a numerical solution of the (2+1)-dimensional coupled Burgers system is studied by using the Homotopy Perturbation Method (HPM). For this purpose, the available analytical solutions obtained by tanh method will be compared to show the validity and accuracy of the proposed numerical algorithm. The results approve the convergence and accuracy of the Homotopy Perturbation Method for numerically analyzed (2+1) coupled Burgers system.     

Numerical solution of the three-dimensional stationary diffraction problem for elastic waves

Three-dimensional problems concerning the propagation of stationary elastic oscillations in media with three-dimensional inclusions are solved numerically. By applying potential theory methods, the original problem is stated as a system of two singular vector integral equations for the unknown internal and external densities of auxiliary sources of waves. An approximate solution of the original problem is obtained by approximating the integral equations by a system of linear algebraic equations, which is then solved numerically. The underlying algorithm has the property of self-regularization, due to which a numerical solution is found without using cumbersome regularizing algorithms. Results of test computations and numerical experiments are presented that characterize the capabilities of this approach as applied to the diffraction of elastic waves in three-dimensional settings.     

倒向随机方程期权定价模型的一类随机算法

期权定价问题可以转化为对倒向随机微分方程的求解,进而转化为对相应抛物型偏微分方程的求解.为了求解与倒向随机微分方程相应的二阶拟线性抛物型微分方程初值问题,引入一类新的随机算法-分层方法取代传统的确定性数值算法.这种数值方法理论上是通过弱显式欧拉法,离散其相应随机系统解的概率表示而得到.该随机算法的收敛性在文中得到证明,其稳定性是自然的.并构造了易于数值实现的基于插值的算法,实证研究说明这种算法能很好地提供期权定价模型的数值模拟.     

A NUMERICALLY STABLE BLOCK MODIFIED GRAM-SCHMIDT ALGORITHM FOR SOLVING STIFF WEIGHTED LEAST SQUARES PROBLEMS

Recently, Wei in proved that perturbed stiff weighted pseudoinverses and stiff weighted least squares problems are stable, if and only if the original and perturbed coefficient matrices A and A^- satisfy several row rank preservation conditions. According to these conditions, in this paper we show that in general, ordinary modified Gram-Schmidt with column pivoting is not numerically stable for solving the stiff weighted least squares problem. We then propose a row block modified Gram-Schmidt algorithm with column pivoting, and show that with appropriately chosen tolerance, this algorithm can correctly determine the numerical ranks of these row partitioned sub-matrices, and the computed QR factor R^- contains small roundoff error which is row stable. Several numerical experiments are also provided to compare the results of the ordinary Modified Gram-Schmidt algorithm with column pivoting and the row block Modified Gram-Schmidt algorithm with column pivoting.     

A method for solving a boundary problem for a nonlinear controlled system

An algorithm is proposed for constructing a control function that transfers a wide class of nonlinear systems of ordinary differential equations from an initial state to an arbitrarily small neighborhood of a given terminal state. The algorithm is convenient for numerical implementation. Taking into account the restrictions on the control and phase coordinates, a constructive criterion is obtained for choosing terminal states for which this transfer is possible. The problem of an interorbital flight is considered and modeled numerically.     

一个寻求解析函数零点的单纯同伦算法及复杂性分析

§1.引言 求解一维实函数的零点,二分法为我们提供了一种有效的整体解法。通常,对于复变函数不仅有实零点,还有复零点,那么能否用二分法的思想来求解复变函数的零点呢?与二分法对应的一个概念是幅角原理,对于直接利用这个原理来确定复函数在某有界区域内零点的问题,虽然作过大量的尝试,但成功者甚少,譬如,Delves-Lyness在[2]中构造的算法,由于反复运算而导致计算效率非常低。D.H.Lehmer对上述原理作了进一     

A Stable and Accurate Numerical Method to Calculate the Motion of a Sharp Interface Between Fluids

Present address: Department of Applied Mathematics, University of Adelaide, G.P.O. Box 498, Adelaide, South Australia 5001. A spectrally accurate numerical method, which is also simpleto implement, is derived to calculate the motion of a fluidinterface. A numerical instability, typical of algorithms forthis problem, is investigated via a linearizing approximationwhich shows that a trivial adjustment of the algorithm rendersit numerically stable while retaining high accuracy. To testfor the correct implementation of the algorithm, non-linearsimultaneous equations are formulated using time derivativeinformation only from the coded procedure, whose solutions describeprogressive interfacial waves of permanent form. The behaviourof this type of algorithm when variations in the point spacingoccurs along the interface is investigated and found to cause"scattering" of travelling wave modes.