Takens—Bogdanov分岐点的分裂迭代算法

本文构造分裂迭代算法用于计算Takens-Bogdanov分岐点,该方法将减少计算的工作量和占用的内存,可以调节的速度线性收敛,并且可以求得Takens-Bogdanov分岐点处fx^及fx^0的广义零特征向量,数值计算说明了算法的有效性。     

二重对称破缺转向点的分裂迭代算法

本文构造分裂迭代算法用于计算二重对称破缺转向点,该方法将明显(?)少计算的工作量和占用的内存,并且以可调节的速度线性收敛。数值计算成功地说明了分裂迭代算法的有效性。     

应用迭代法求解一类非线性问题

本文应用迭代法求解一类有限维非线性问题,该方法是求解线性问题的雅可比迭代法在非线性问题上的推广,且此迭代方法具有几何收敛性质.     

A Simultaneous Iteration Method for the Unsymmetric Eigenvalue Problem

This paper describes a method of obtaining all or a dominantsubset of the eigenvalues and corresponding left and right-handeigenvectors of unsymmetric matrices by simultaneous iteration.The method differs from Bauer's biiteration in that re-orientationof the trial vectors is achieved at each iteration by performingan "interaction analysis".     

非线性问题的参数迭代求解法

提出一种对非线性问题的参数迭代求解法,算例表明,其一次迭代解便有很好的精度.     

一类高阶牛顿迭代法及其在线性互补问题中的应用

通过等价转换,把线性互补问题转化为一个不可微的非线性方程组,进而采用光滑函数处理,得到一个光滑非线性方程组,利用高阶牛顿迭代法进行求解.该方法不再区分线性互补问题是否单调,因此扩大了线性互补问题的求解范围.计算结果表明,方法计算速度快,对线性互补问题求解较为有效.     

Bifurcation of Positive Solutions for a Nonlocal Problem

In this paper, we study bifurcation of positive solutions for a nonlocal problem in a bounded domain. Using the degree argument and variational method, we obtain two results about bifurcation of positive solutions.     

Two-Stage Multisplitting Iteration Methods Using Modulus-Based Matrix Splitting as Inner Iteration for Linear Complementarity Problems

The matrix multisplitting iteration method is an effective tool for solving large sparse linear complementarity problems. However, at each iteration step we have to solve a sequence of linear complementarity sub-problems exactly. In this paper, we present a two-stage multisplitting iteration method, in which the modulus-based matrix splitting iteration and its relaxed variants are employed as inner iterations to solve the linear complementarity sub-problems approximately. The convergence theorems of these two-stage multisplitting iteration methods are established. Numerical experiments show that the two-stage multisplitting relaxation methods are superior to the matrix multisplitting iteration methods in computing time, and can achieve a satisfactory parallel efficiency.     

A Fast Algorithm for Solving a Simple Search Problem

Computational Mathematics and Mathematical Physics - A fast algorithm for solving the Danskin problem is proposed. The dependence of its solution on parameters is analyzed.     

The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

In this paper,by means of constructing the linear complementarity problems into the corresponding absolute value equation,we raise an iteration method,called as...     

The Splitting Problem for Coalgebras: A Direct Approach

In this note we give a new and elementary proof of a result of Năstăsescu and Torrecillas (J. Algebra, 281:144–149, 2004) stating that a coalgebra C is finite dimensional if and only if the rational part of any right module M over the dual algebra is a direct summand in M (the splitting problem for coalgebras). Research supported by a CNCSIS BD-type grant, and by the bilateral project BWS04/04 “New Techniques in Hopf Algebra Theory and Graded Ring Theory” of the Flemish and Romanian governments.     

一种两点迭代法

本文给出了一个求超越方程实根的新的两点格式ｘｋ＋１＝ｘｋ－ｘｋ－ｘｋ－１３ｆ（ｘｋ）－４ｆｘｋ＋ｘｋ－１２＋ｆ（ｘｋ－１）ｆ（ｘｋ），它集弦割法和抛物线法的优点于一身，具有更快的收敛速度，且收敛阶为二阶．     

A Direct Method for Pitchfork Bifurcation Points

To overcome the difficulty caused by the singularity at the pitchfork bifurcation points, we introduce the homotopy parameter so that the problem of computing the pitchfork bifurcation points can be transferred to that of computing the fold points of degree 3 with respect to the homotopy parameter. An extended system for pitchfork bifurcation points is given. The regularity of the extended system is proved. Finally, the numerical examples show the effectiveness of our method.     

Optimization of the Hermitian and Skew-Hermitian Splitting Iteration for Saddle-Point Problems

We study the asymptotic rate of convergence of the alternating Hermitian/skew-Hermitian iteration for solving saddle-point problems arising in the discretization of elliptic partial differential equations. By a careful analysis of the iterative scheme at the continuous level we determine optimal convergence parameters for the model problem of the Poisson equation written in div-grad form. We show that the optimized convergence rate for small mesh parameter h is asymptotically 1–O(h ^1/2). Furthermore we show that when the splitting is used as a preconditioner for a Krylov method, a different optimization leading to two clusters in the spectrum gives an optimal, h-independent, convergence rate. The theoretical analysis is supported by numerical experiments.This revised version was published online in October 2005 with corrections to the Cover Date.     

A Heuristic Method for a Job-Scheduling Problem

A batch of jobs is to be processed on a certain production line. Each job can be done in several states of the line but at varying production costs and there is also a cost of changing states. The batch is to be scheduled at minimum total cost. A method of breaking down the problem and using a branching process to generate sequences of states is given. It takes advantage of special features of the cost structure.     

改进的最佳摄动量法及在反问题中的应用

给出了改进的最佳摄动量法,并应用在双曲型方程参数反演问题的求解中.由遗传算法借助交叉和变异算子控制全局搜索来获得参数的初始迭代值,代入最佳摄动量法求解出稳定的高精度数值解.     

A Parallel Splitting Method for Separable Convex Programs

In this paper, we propose a new parallel splitting augmented Lagrangian method for solving the nonlinear programs where the objective function is separable with three operators and the constraint is linear. The method is an improvement of the method of He (Comput. Optim. Appl., 2(42):195–212, 2009), where we generate a predictor using the same parallel splitting augmented Lagrangian scheme as that in He (Comput. Optim. Appl., 2(42):195–212, 2009), while adopting a new strategy to get the next iterate. Under the mild assumptions of convexity of the underlying mappings and the non-emptiness of the solution set, we prove that the proposed algorithm is globally convergent. We apply the new method in the area of image processing and to solve some quadratic programming problems. The preliminary numerical results indicate that the new method is efficient.     

一个数学建模问题的简单解法

银行利率给出了一个简单计算方法 ,这种方法更符合中学生思维的习惯 .     

2n阶Lidstone边值问题正解的逐次迭代

研究了2n阶Lidstone边值问题正解的逐次迭代,其中非线性项依赖于所有偶数阶导数.通过考察非线性项在某些有国介集合上的“高度”并利用单调迭代方法构造了一个逐次迭代程序.这个迭代程序从一个多项式开始并且是可行的.使用这个结论获得了m个正解的迭代方法,其中m是一个任意的自然数.