含非线性源项的变分不等式的加性区域分解法

本文研究一类求解非线性变分不等式的加性区域分解法,其中区域分解为非重叠子区域,在界面上采用Robin条件,得到了算法的收敛性,而且数值算例表明,选取适合的Robin参数可加快算法的收敛速度.     

有限元奇性问题的自适应处理

§1.引言 有限元奇性问题(包括凹角域问题以及方程本身的奇性等问题),由于奇点的存在,致使奇点附近收敛速度明显减慢。处理这一问题的有效方法是构作可靠实用的后验估计量来寻找收敛慢的坏单元,进行局部加密剖分,从而以最快的速度提高整体精度,但工作量最小。 本文的特点在于:1.对剖分条件限制较弱,只要求正规剖分(regular meshes)即     

外部非定常Navier-Stokes方程的非线性Galerkin算法

提出了求解外部非定常Navier-stokes方程的有限元边界元耦合的非线性Galerkin算法,证明了相应变分问题的正则性和数值解的收敛速度。收敛性分析表明如果选取粗网格尺度H是细网格尺度h的开平方数量级,则该算法提供了与古典Galerkin算法同阶的收敛速度。然而非线性Galerkin算法仅仅需要在粗网格解非线性问题,在细网格上解线性问题。因此,该算法可以节省计算工作量。     

精细辛几何算法的误差估计

该文讨论了精细辛几何算法的计算误差,先展开二阶和四阶精细辛几何算法的表达式得到误差同精细剖分数目的关系,然后分析了任意阶精细辛几何算法的误差,得到了一致简洁的结果,总的误差可近似表示为单个精细步长的误差乘以剖分数目,最后讨论了在要求控制精度下剖分数目的选取,该方法克服了算法精度对积分时间步长的依赖性.     

关于解非线性方程组Krawczyk算法的进一步研究

本文应用区间矩阵知识,讨论了具区间—Lipschitz矩阵的非线性方程组解的存在性以及求解的Krawczyk算法的收敛性条件;同时,改进了Krawczyk算法的构造,得到了二阶收敛速度。     

非一致分布下的在线分位数回归算法

本文在非一致抽样分布下,研究与高斯核有关的在线分位数算法的收敛阶.本文引入阈值到Pinball损失函数产生算法的稀疏性,用H?lder对偶空间刻画抽样分布的非一致性,通过误差分解和迭代方法推导算法的收敛速度.并且以中位数回归为例,得到算法的具体收敛速度,同时也指明本文的背景和数学方法适用于一般分位数回归.     

一种求解化工动态优化问题的改进磷虾觅食优化算法

智能算法原理简单、容易实现,且具有良好的全局收敛能力,近年来被广泛应用于化工过程的动态优化问题.提出一种改进的磷虾觅食优化算法求解化工动态优化问题.该算法通过跟踪磷虾种群的变化来更新速度因子,提高收敛速度;引入自适应柯西变异,增强了算法跳出局部最优值的能力.针对化工动态优化问题,首先通过控制向量参数化方法将其转化为非线性规划问题,并引入变时间区间分布法来优化区间划分,然后利用改进算法进行求解.最后,将改进算法应用于多个化工动态优化问题中,仿真结果表明,该算法具有良好的可行性.     

基于正余双弦自适应灰狼优化算法的医药物流配送路径规划

针对传统灰狼优化算法易早熟收敛陷入局部最优和收敛速度慢的缺陷,提出一种正余双弦自适应灰狼优化算法.首先,在灰狼捕食阶段引入正弦搜索,增强算法的全局勘探能力,减少算法的搜索盲点,提高算法的搜索精度.在引入正弦搜索的同时,引入余弦搜索,增强算法的局部开发能力,提高算法的收敛速度.其次,在搜索过程中加入自适应交叉变异机制,通过适应度值的大小自适应选取交叉变异概率,有效的提高了粒子跳出局部最优的概率.通过数值对比试验,验证了改进算法具有较强的收敛精度和收敛速度.     

一类非光滑总体极值的区间算法

本文利用区间分析知识 ,构造了一类 n维非光滑函数总体极值的区间算法 ,理论分析和实例计算均表明本文算法安全可靠 ;能求出全部总体极小点 ;收敛速度也比以前方法[1] 明显加快     

解非线性方程组的两种区间迭代法

本文为改善(Ⅱ)的计算量、计算稳定性、收敛区域和收敛速度对(Ⅱ)作了修改,提出了两种修改算法。 文章中小写字母表示实空间中的数、向量、矩阵和函数,大写字母表示区间、区间向量、区间矩阵和区间函数。如果区间矩阵的左、右端点矩阵为、,则记=[a,     

DECUHR: an algorithm for automatic integration of singular functions over a hyperrectangular region

We describe an automatic cubature algorithm for functions that have a singularity on the surface of the integration region. The algorithm combines an adaptive subdivision strategy with extrapolation. The extrapolation uses a non-uniform subdivision that can be directly incorporated into the subdivision strategy used for the adaptive algorithm. The algorithm is designed to integrate a vector function over ann-dimensional rectangular region and a FORTRAN implementation is included.Supported by the Norwegian Research Council for Science and the Humanities.     

CORNER-CUTTING SUBDIVISION SURFACES OF GENERAL DEGREES WITH PARAMETERS

As a corner-cutting subdivision scheme, Lane-Riesefeld algorithm possesses the concise and unified form for generating uniform B-spline curves: vertex splitting plus repeated midpoint averaging. In this paper, we modify the second midpoint averaging step of the Lane-Riesefeld algorithm by introducing a parameter which controls the size of corner cutting, and generalize the strategy to arbitrary topological surfaces of general degree. By adjusting the free parameter, the proposed method can generate subdivision surfaces with flexible shapes. Experimental results demonstrate that our algorithm can produce subdivision surfaces with comparable or even better quality than the other state-of-the-art approaches by carefully choosing the free parameters.     

Multiobjective Search Algorithm with Subdivision Technique

This paper presents a multiobjective search algorithm with subdivision technique (MOSAST) for the global solution of multiobjective constrained optimization problems with possibly noncontinuous objective or constraint functions. This method is based on a random search method and a new version of the Graef-Younes algorithm and it uses a subdivision technique. Numerical results are given for bicriterial test problems.     

Condition number based complexity estimate for computing local extrema

In this paper, we present a new algorithm for computing local extrema by modifying and combining algorithms in symbolic and numerical computation. This new algorithm improves the classical steepest descent method that may not terminate, by combining a Sturm’s theorem based separation method and a sufficient condition on infeasibility. In addition, we incorporate a grid subdivision method into our algorithm to approximate all local extrema. The complexity of our algorithm is polynomial in a newly defined condition number, and singly exponential in the number of variables.     

A Branch and Bound Algorithm for Separable Concave Programming

In this paper, we propose a new branch and bound algorithm for the solution of large scale separable concave programming problems. The largest distance bisection (LDB) technique is proposed to divide rectangle into sub-rectangles when one problem is branched into two subproblems. It is proved that the LDB method is a normal rectangle subdivision(NRS). Numerical tests on problems with dimensions from 100 to 10000 show that the proposed branch and bound algorithm is efficient for solving large scale separable concave programming problems, and convergence rate is faster than ω-subdivision method.     

Adaptive Isotopic Approximation of Nonsingular Curves: the Parameterizability and Nonlocal Isotopy Approach

We consider domain subdivision algorithms for computing isotopic approximations of a nonsingular algebraic curve. The curve is given by a polynomial equation f(X,Y)=0. Two algorithms in this area are from Snyder (1992) SIGGRAPH Comput. Graphics, 26(2), 121 and Plantinga and Vegter (2004) In Proc. Eurographics Symposium on Geometry Processing, pp. 245–254. We introduce a new algorithm that combines the advantages of these two algorithms: like Snyder, we use the parameterizability criterion for subdivision, and like Plantinga and Vegter, we exploit nonlocal isotopy. We further extend our algorithm in two important and practical directions: first, we allow subdivision cells to be rectangles with arbitrary but bounded aspect ratios. Second, we extend the input domains to be regions R ₀ with arbitrary geometry and which might not be simply connected. Our algorithm halts as long as the curve has no singularities in the region, and intersects the boundary of R ₀ transversally. Our algorithm is practical and easy to implement exactly. We report some very encouraging experimental results, showing that our algorithms can be much more efficient than the algorithms of Plantinga–Vegter and Snyder.     

An efficient algorithm for range computation of polynomials using the Bernstein form

We present a novel optimization algorithm for computing the ranges of multivariate polynomials using the Bernstein polynomial approach. The proposed algorithm incorporates four accelerating devices, namely the cut-off test, the simplified vertex test, the monotonicity test, and the concavity test, and also possess many new features, such as, the generalized matrix method for Bernstein coefficient computation, a new subdivision direction selection rule and a new subdivision point selection rule. The features and capabilities of the proposed algorithm are compared with those of other optimization techniques: interval global optimization, the filled function method, a global optimization method for imprecise problems, and a hybrid approach combining simulated annealing, tabu search and a descent method. The superiority of the proposed method over the latter methods is illustrated by numerical experiments and qualitative comparisons.     

Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.     

插值细分曲线有理参数点的精确求值

本文提出了求值插值细分曲线上任意有理参数的算法.通过构造与细分格式相关的矩阵,m进制分解给定有理数以及特征分解循环节对应算子乘积,计算得到控制顶点权值,实现对称型静态均匀插值细分曲线的求值.本文给出了四点细分和四点Ternary细分曲线的求值实例.算法可以推广到求值其他非多项式细分格式中.