A hybrid method for inverse cavity scattering problem for shape

In this paper, we give a hybrid method to numerically solve the inverse open cavity scattering problem for cavity shape, given the scattered solution on the opening of the cavity. This method is a hybrid between an iterative method and an integral equations method for solving the Cauchy problem. The idea of this hybrid method is simple, the operation is easy, and the computation cost is small. Numerical experiments show the feasibility of this method, even for cases with noise.     

对流扩散方程的有限体积-有限元方法的误差估计

本文结合有限体积方法和有限元方法处理非线性对流扩散问题,非线性对流项利用有限体积方法处理,扩散项利用有限元方法离散,并给近似解的误差估计。     

Algorithms for the CMRH method for dense linear systems

The CMRH (Changing Minimal Residual method based on the Hessenberg process) method is a Krylov subspace method for solving large linear systems with non-symmetric coefficient matrices. CMRH generates a (non orthogonal) basis of the Krylov subspace through the Hessenberg process, and minimizes a quasi-residual norm. On dense matrices, the CMRH method is less expensive and requires less storage than other Krylov methods. In this work, we describe Matlab codes for the best of these implementations. Fortran codes for sequential and parallel implementations are also presented.     

Multiplicative Extrapolation Method for Constructing Higher Order Schemes for Ordinary Differential Equations

IntroductionWhenweconstructahigherorderschemeforsystemsofordinarydifferentialequations:y,=f(y)(1)(wherey=y(x),andxisavariable),weoftenusethe"Tayorseriesexpanding"method,butsometimesthismethodisverytediouswhenitisaPpliedtogethigherorderschemes.Thereisanothermethod:Lieseries,itisthemethodweuseinthispaPer.J.Dragt,F,Neri,andStaulySteinberghavedonealotofworkindevelopingthismethod.Fordetails,onecanreferto[4,6,8].WejustaPplythismethodtoourproblem,anddonotneedtocomputeouttheexacttermsofthe"Lieser…     

Asymptotic Initial-Value Method for Singularly-Perturbed Boundary-Value Problems for Second-Order Ordinary Differential Equations

A computational method is presented to solve a class of nonturning-point singularly-perturbed two-point boundary-value problems for second-order ordinary differential equations with a small parameter multiplying the highest derivative, subject to Dirichlet-type boundary conditions. In this method, first we construct a zeroth order asymptotic expansion for the solution of the given boundary-value problem. Then, this problem is integrated to get an equivalent initial-value problem for first-order ordinary differential equations. This initial-value problem is solved by either a classical method or a fitted operator method after approximating some of the terms in the differential equations by using the zeroth order asymptotic expansion. This method is effective and easy to implement. An error estimate is derived for the numerical solution. Examples are given to illustrate the method.     

Cardinal functions for Legendre pseudo-spectral method for solving the integro-differential equations

In this article, we present a new numerical method to solve the integro-differential equations (IDEs). The proposed method uses the Legendre cardinal functions to express the approximate solution as a finite series. In our method the operational matrix of derivatives is used to reduce IDEs to a system of algebraic equations. To demonstrate the validity and applicability of the proposed method, we present some numerical examples. We compare the obtained numerical results from the proposed method with some other methods. The results show that the proposed algorithm is of high accuracy, more simple and effective.     

Linearized ridge-path method for function minimization

A modification based on a linearization of a ridge-path optimization method is presented. The linearized ridge-path method is a nongradient, conjugate direction method which converges quadratically in half the number of search directions required for Powell's method of conjugate directions. The ridge-path method and its modification are compared with some basic algorithms, namely, univariate method, steepest descent method, Powell's conjugate direction method, conjugate gradient method, and variable-metric method. The assessment indicates that the ridge-path method, with modifications, could present a promising technique for optimization.This work was in partial fulfillment of the requirements for the MS degree of the first author at Cairo University, Cairo, Egypt. The authors would like to acknowledge the helpful and constructive suggestions of the reviewer.     

A Method for Constructing Coreflections for Nearness Frames

We provide a fairly general method, which is straightforward and widely applicable, for constructing some coreflections in the category of nearness frames. The method captures all coreflective subcategories with 1???1 coreflection maps; this includes the well-known uniform, totally bounded and separable coreflections. The primary application of this method answers in the affirmative the question of Dube and Mugochi [15] as to whether strong nearness frames are coreflective in nearness frames. We show that the strong coreflection can change the underlying frame, in contrast to Dube and Mugochi’s almost uniform coreflection in the category of interpolating nearness frames. The method also finds application in categories other than nearness frames, for instance, prenearness frames and nearness σ-frames. We conclude with an application to the unstructured setting where we recover the regular and completely regular coreflections in frames.     

Convergence rates for Kaczmarz-type algorithms

By making use of the normal and skew-Hermitian splitting (NSS) method as the inner solver for the modified Newton method, we establish a class of modified Newton-NSS method for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices at the solution points. Under proper conditions, the local convergence theorem is proved. Furthermore, the successive-overrelaxation (SOR) technique has been proved quite successfully in accelerating the convergence rate of the NSS or the Hermitian and skew-Hermitian splitting (HSS) iteration method, so we employ the SOR method in the NSS iteration, and we get a new method, which is called modified Newton SNSS method. Numerical results are given to examine its feasibility and effectiveness.     

对多等级质量产品（以σ衡量）抽样数n值的计算及分极标准的制定方法

本文利用抽样分布理论，对以σ衡量质量的多等级产品质量检验问题，提出了一个具体的处理方法，该方法给出了计算抽样数的公式，也给出了确定各等级之间距离的计算方法，揭示了抽样置信度、抽样数ｎ、等级距离三者之间的关系。并按本文的方法，提出了对广东商检局出口桑蚕丝原抽样方案的修改意见。     

A wider convergence area for the MSTMAOR iteration methods for LCP

In this paper, based on the Hermitian and skew-Hermitian splitting, we give a generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method to solve singular complex symmetric linear systems, this method has two parameters. We give the semi-convergent conditions, and some numerical experiments are given to illustrate the efficiency of this method.     

鞍点问题的修正对称超松弛迭代算法

为了提高求解鞍点问题的迭代算法的速度,通过设置合适的加速变量,对修正超松弛迭代算法（简记作MSOR-like算法）和广义对称超松弛迭代算法（简记作GSSOR-like算法）进行了修正,给出了修正对称超松弛迭代算法,即MSSOR-like （modified symmetric successiveover-relaxation）算法,并研究了该算法收敛的充分必要条件.最后,通过数值例子表明,选择合适的参数后,新算法的迭代速度和迭代次数均优于MSOR-like （modified successive overrelaxation）和GSSOR-like （generalized symmetric successive over-relaxation）算法,因此,它是一种较好的解决鞍点问题的算法.     

Dodd-Bullough-Mikhailov方程的精确解

利用(G'/G)法求解了Dodd-Bullough-Mikhailov的精确解,得到了Dodd-Bullough-Mikhailov方程的用双曲函数,三角函数和有理函数表示的三类精确行波解.由于方法中的G为某个二阶常系数线性ODE的通解,故方法具有直接、简洁的优点;更重要的是,方法可用于求得其它许多非线性演化方程的行波解.如果对其中双曲函数表示的行波解中的参数取特殊值,那么可得已有的孤波解.     

An efficient method for solving difference systems for elliptic differential equations

A method for solving systems of linear algebraic equations arising in connection with the approximation of boundary value problems for elliptic partial differential equations is proposed. This method belongs to the class of conjugate directions method applied to a preliminary transformed system of equations. A model example is used to explain the idea underlying this method and to investigate it. Results of numerical experiments that confirm the method’s efficiency are discussed.     

Directional secant method for nonlinear equations

We present a directional secant method, a secant variant of the directional Newton method, for solving a single nonlinear equation in several variables. Under suitable assumptions, we prove the convergence and the quadratic convergence speed of this new method. Numerical examples show that the directional secant method is feasible and efficient, and has better numerical behaviour than the directional Newton method.     

A quadrature based method for evaluating exponential-type functions for exponential methods

We present a quadrature-based method to evaluate exponential-like operators required by different kinds of exponential integrators. The method approximates these operators by means of a quadrature formula that converges like O(e ^−cK ), with K the number of quadrature nodes, and it is useful when solving parabolic equations. The approach allows also the evaluation of the associated scalar mappings. The method is based on numerical inversion of sectorial Laplace transforms. Several numerical illustrations are provided to test the algorithm, including examples with a mass matrix and the application of the method inside the MATLAB package EXP4, an adaptive solver based on an exponential Runge–Kutta method.     

A New defy for iteration methods

The work presents an adaptation of iteration method for solving a class of thirst order partial nonlinear differential equation with mixed derivatives.The class of partial differential equations present here is not solvable with neither the method of Green function, the most usual iteration methods for instance variational iteration method, homotopy perturbation method and Adomian decomposition method, nor integral transform for instance Laplace,Sumudu, Fourier and Mellin transform. We presented the stability and convergence of the used method for solving this class of nonlinear chaotic equations.Using the proposed method, we obtained exact solutions to this kind of equations.     

多风险因素的投标报价决策方法

本文讨论工程项目投标报价的多风险因素层次模型，系统地介绍了90年代以来发展出的多风险因素条件下投标报价的5种主要决策方法，即层次分析法（AHP）、人工神经网络（ANN）、模糊评价法（Fuzzy）、专家系统（ES）和基于事例推理（CBR）。本文也对中国在该领域的研究现状作一个简单的评述。     

Iterative Methods of Richardson-Lucy-Type for Image Deblurring

Image deconvolution problems with a symmetric point-spread function arise in many areas of science and engineering. These problems often are solved by the Richardson-Lucy method, a nonlinear iterative method. We first show a convergence result for the Richardson-Lucy method. The proof sheds light on why the method may converge slowly. Subsequently, we describe an iterative active set method that imposes the same constraints on the computed solution as the Richardson-Lucy method. Computed examples show the latter method to yield better restorations than the Richardson-Lucy method and typically require less computational effort.     

Iterative approximate factorization for difference operators of high-order bicompact schemes for multidimensional nonhomogeneous hyperbolic systems

An iterative method for solving equations of multidimensional bicompact schemes based on an approximate factorization of their difference operators is proposed for the first time. Its algorithm is described as applied to a system of two-dimensional nonhomogeneous quasilinear hyperbolic equations. The convergence of the iterative method is proved in the case of the two-dimensional homogeneous linear advection equation. The performance of the method is demonstrated on two numerical examples. It is shown that the method preserves a high (greater than the second) order of accuracy in time and performs 3–4 times faster than Newton’s method. Moreover, the method can be efficiently parallelized.