用人工神经网络求解非线性方程组的一种方法

本文探讨用人工神经网络的反向传播算法求解非线性方程组,计算量小,简便易行并给出计算机仿真结果,所得到的解令人满意。     

求解非线性方程组的异步并行 拟牛顿迭代算法的收敛性分析

本文给出了MIMD多处理机上的求解非线性方程组的异步并行拟牛顿迭代算法的收敛性分析,给出了收敛的充分性条件。     

解一元非线性方程的线性二次插值方法

许多问题的数值计算最终都归化成求解一元非线性方程,数值计算的有效性取决于求解这个非线性方程的算法。本文构造了求解一元非线性方程的线性二次插值方法,它既保持了线性插值的可靠性,又保持了二次插值的收敛速度。文中给出算法的构造思想、计算步骤和程序实现框图。将该算法应用到变截面梁横向振动固有频率的计算,得到较好的效果。     

求解非线性最小二乘全局解基于最速下降法和遗传算法的混合算法

本文通过在遗传算法中嵌入一个最速下降算子,并定义适应度函数、选择算子和数据结构,从而得到可结合遗传算法和最速下降法两者长处,既有较快收敛性,又能以较大概率求得非线性最小二乘问题全局解的混合算法.数值计算表明该方法显著优于遗传算法和最速下降法.     

线性定常系统离散状态方程的递推求解算法

本文利用简单的数学知识,基于连续系统的模型,实现了离散时间系统状态方程的递推求解。算法同时可获得系统的脉冲响应函数,实现连续系统的离散化。仿真结果是令人满意的。     

求解线性不等式组的仿射梯度算法

设计了一种新的求解线性不等式的动力系统方法－仿射梯度算法，算法不改变原问题的稀疏性，每步迭代的计算量较小，只包含简单的算术运算，具有很好的计算时间和存储空间的性质，有利于解决大规模稀疏的能源规划问题，给出了算法的动力系统的连续和离散时间模型，并证明了模型具有渐进稳定性，数值实验结果表明，此算法是有效的。     

机器人关节变量的多微机并行算法

本文对机器人控制器运动学求逆运动学关节角的运算进行了并行算法研究,并在共享存储器结构的三台及四台Z80-Ⅱ型单板机构成的多机系统上实现了这一算法。这一研究目的是为了分析在机器人控制器的大量计算中如何提高运算速度及并行效率。实验表明该方法对解机器人某些问题是可行的,采用本算法无论在速度还是在效率上都较其它算法占优势。     

基于矩阵分解的惯导安装误差矩阵解耦方法

针对捷联惯性导航系统级标定中安装误差矩阵存在3组耦合关系问题,提出一种基于矩阵分解的解耦方法。该方法将安装误差矩阵分解为对称误差矩阵和斜对称误差矩阵后,推导其对惯性导航姿态方程和速度方程的影响,揭露系统级标定中安装误差矩阵存在耦合的原因——陀螺仪表组和加速度计仪表组的斜对称误差对误差方程的影响是耦合的,进而提出适当选取体坐标系使得陀螺仪表组的斜对称误差矩阵为0的解耦方法。该解耦方法是一种均值分配方法,与传统解耦方法相比能减少系统运算中的二阶舍项误差。仿真实例说明了该解耦方法是有效的。     

群决策问题的一种求解方法

本文提出了一种求解各决策问题的模型。首先，每个决策者给出对候选方案偏好度量，然后求解群体的偏好序以使所有决策者对群体序的不满意度最小。本文还给出了模型的求解算法。     

求解常微分方程的一类线性多步方法

本文给出常微分方程y′=f(t,y)及″=f(t,y)的一类线性多步方法,它们的系数容易在计算机上生成。     

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE STOKES AND NAVIER-STOKES EQUATIONS PART I. THE LINEAR CASE

1 IntroductionDuring the past decade, many stabilized finite element methods were designed for solvingproblems arising from fluid and solid mechanics. For example, the Navier--Stokes problem hasbeen playing an active role in the development of stabilized methods, e.g. see [1--6], etc andreferences therein. It is well known that the standard GaJerkin method for the Navier--Stokesproblem is subject to two main obstacles. One comes from the high Reynolds nUmber or highadvection, or the limiti…     

A ROBUST DECOMPOSITION OF LINEAR PROGRAMMING USING A GOAL-PARTITIONING METHOD

The Dantzig/Wolfe linear programming decomposition algorithm has had important economicinterpretations as well as a widespread impact on solving large scale linear programming problem.Inthis paper we consider a similar underlying structure,where however there is only one couplinginequality or equation.With this simplification,we demonstrate how to achieve an equitable partitionof the overall coupling resource to individual subproblem constraints through a simple iterationprocedure which appears to be very efficient.     

A HYBRID METHOD FOR LINEAR PROGRAMMING

1.IntroductionItiswellknownthatsinceKaxmarkax[1]proposedthefirstinferiorpoilltmethod,manyexpertshavebeeninvolvedtoimproveandcompletethismethod.ThereisalotofprogressinthisareaandmanyinteriorpointmethodsaredevelOPed;theinterestedreaderisreferredtotheexcellentbooksofhoandPllthenpura[2]andNesterovandNemirovskiil3].TheseiDteriorpointmethodscanbeclassifiedroughlyintothreecategories:(i)potentialreduction,(n)affinescaling,and(iii)path-following.Theaffine-scalingmethodisshowntoworkwellinpracticebyta…     

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE STOKES AND NAVIER-STOKES EQUATIONS PART II. THE NONLINEAR CASE

1 IntroductionIt is necessary to make some conuneots on some of the re1ated methodologies lately emp1oyedto stabilize the Ga1erkin finite e1ement method for the incompressible NavierStokes equations,including the Stokes equation and the advectiondiffusion problem. Owing to the fact that thehigh Reynold number amounts to a small diffusive term in the advection--diffusion problem,here we will repeatedly mention the diffosion, not the Reynold number or the viscosity in the.. Jincompressible Na…     

A CUTTING PLANE METHOD FOR LINEAR BILEVEL PROGRAMS

1.IntroductionThebilevelprogr~ngproblem(BLPP),anoptimizationproblemwithaspecialconstraintfunctionwhichisimplicitlydeterminedbyanotheroptimizationproblem,hasreceivedmuchatteDtionofresearchersduringthelastdecade.Falkll]pioneeredtheworkbystudyingthegeneralmad-minproblem,aspecialcaseoflinearBLPP,andproposedamethodbasedonbranch-and-boundandlinearprogrammingtechniques.BialasandKar.an[2]investigatedthegeometricpropertiesofthefeasibleregionofthelinearBLPPandshowedthatsolutionsoftheproblemmayoccu…     

ON THE EXISTENCE OF MEROMORPHIC SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

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A NEWTON MULTIGRID METHOD FOR QUASILINEAR PARABOLIC EQUATIONS

A combination of the classical Newton Method and the multigrid method, i.e., a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O（NNk） similar to multigrid method for linear parabolic problems.     

ON A LINEAR EQUATIONS METHOD OF NONLINEAR POLYNOMIAL EQUATIONS-SOLVING

A method for solving nonlinear polynomial equations is given which avoids theappearance of redundant factors as in the previous characteristic set method developed bythe present author. The new method seems thus to be of much higher efficiency than theprevious one. It has the further advantage that numerical data may be inserted at willeither at the outset or during the procedure so far removal of factors by divisions may beavoided.     

NONLINEAR GALERKIN METHOD FOR STEADYNONLINEAR DIFFERENTIAL EQUATIONS

1.IntroductionNonlinearGalerkinmethodsarenumericalschemesforthedissipativeevolutionpartialdifferelltialequationswherethespatialdiscretizationreliesonanonlinearmanifoldinsteadofalinearspaceasintheclassicalGalerkinmethod.Moreprecisely,oneconsidersafinitedim…