一类高阶有理差分方程解的收敛性(英文)

本文考查下列高阶有理差分方程xn+1=(α+B1xn-1+B3xn-3+…+B2k+1xn-2k-1)/(A+B0xn+B2xn-2+…+B2kxn-2k,),n=0,1,…,其中k是非负整数,参数α,A,Bi,i=0,1,2,…,2k+1和初始值x-2k-1,x-2k,x-2k+1,…,x0是非负实数.给出充分条件,在此条件下当且仅当∑k+1i=1B2i-1=A时,方程的每个解收敛于方程的一个二周期解.     

解非线性规划问题的不精确线性搜索SQP滤子方法

本文用序列二次规划方法(SQP)结合Wolfe-Powell不精确线性搜索准则求解非线性规划问题.Wolfe-Powell准则是一种能够使目标函数获得充分下降而运行时间较省的确定步长方法.不精确线性搜索滤子方法比较其它结合精确线性搜索和信赖域方法求解问题的滤子方法更灵活更易实现.如果目标函数的预测下降量为负,我们的工作将主要利用可行恢复项改善可行性.一般条件下,本文提出的算法较易实现,且具有全局收敛性.数值试验显示了算法的有效性.     

Hermite Subdivision Schemes and Taylor Polynomials

We propose a general study of the convergence of a Hermite subdivision scheme ℋ of degree d>0 in dimension 1. This is done by linking Hermite subdivision schemes and Taylor polynomials and by associating a so-called Taylor subdivision (vector) scheme . The main point of investigation is a spectral condition. If the subdivision scheme of the finite differences of is contractive, then is C ⁰ and ℋ is C ^d . We apply this result to two families of Hermite subdivision schemes. The first one is interpolatory; the second one is a kind of corner cutting. Both of them use the Tchakalov-Obreshkov interpolation polynomial.      

求解非线性中立型延迟微分方程一类线性多步方法的收敛性

本文致力于带有Lagrang插值的一类线性多步法求解非线性中立型延迟微分方程的误差分析.证明了一个p′阶的线性多步方法配上一个q阶的Lagrang插值导致一个minf[p′,q 1]阶的E-(或EB-)收敛的非线性中立型延迟微分方程数值方法.     

Expected Residual Minimization Method for Stochastic Variational Inequality Problems

This paper considers a stochastic variational inequality problem (SVIP). We first formulate SVIP as an optimization problem (ERM problem) that minimizes the expected residual of the so-called regularized gap function. Then, we focus on a SVIP subclass in which the function involved is assumed to be affine. We study the properties of the ERM problem and propose a quasi-Monte Carlo method for solving the problem. Comprehensive convergence analysis is included as well. This work was supported in part by SRF for ROCS, SEM and Project 10771025 supported by NSFC.     

On convergent numerical algorithms for unsymmetric collocation

In this paper, we are interested in some convergent formulations for the unsymmetric collocation method or the so-called Kansa’s method. We review some newly developed theories on solvability and convergence. The rates of convergence of these variations of Kansa’s method are examined and verified in arbitrary–precision computations. Numerical examples confirm with the theories that the modified Kansa’s method converges faster than the interpolant to the solution; that is, exponential convergence for the multiquadric and Gaussian radial basis functions (RBFs). Some numerical algorithms are proposed for efficiency and accuracy in practical applications of Kansa’s method. In double–precision, even for very large RBF shape parameters, we show that the modified Kansa’s method, through a subspace selection using a greedy algorithm, can produce acceptable approximate solutions. A benchmark algorithm is used to verify the optimality of the selection process.     

求解2×2块对称不定线性方程组迭代法的收敛性分析

本文研究求解系数矩阵为2×2块对称不定矩阵时的线性方程组,提出了一种新的分裂迭代法,并通过研究迭代矩阵的谱半径,详细讨论了新方法的收敛性.最后,我们也讨论了预条件矩阵特征根的几条性质.     

Cavitation,Invertibility, and Convergence of Regularized Minimizers in Nonlinear Elasticity

We prove that energy minimizers for nonlinear elasticity in which cavitation is allowed only at a finite number of prescribed flaw points can be obtained, in the limit as ε→0, by introducing micro-voids of radius ε in the domain at the prescribed locations and minimizing the energy without allowing for cavitation. This extends the result by Sivaloganathan, Spector, and Tilakraj (SIAM J. Appl. Math. 66:736–757, 2006) to the case of multiple cavities, and constitutes a first step towards the numerical simulation of cavitation (in the nonradially-symmetric case).      

Convergence in Conformal Field Theory

Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. The author reviews some main convergence results, conjectures and problems in the construction and study of conformal field theories using the representation theory of vertex operator algebras. He also reviews the related analytic extension results, conjectures and problems. He discusses the convergence and analytic extensions of products of intertwining operators (chiral conformal fields) and of q-traces and pseudo-q-traces of products of intertwining operators. He also discusses the convergence results related to the sewing operation and the determinant line bundle and a higher-genus convergence result. He then explains conjectures and problems on the convergence and analytic extensions in orbifold conformal field theory and in the cohomology theory of vertex operator algebras.     

ON THE CONVERGENCE OF THE PARABOLIC APPROXIMATION OF A CONSERVATION LAW IN SEVERAL SPACE DIMENSIONS

1.IntrodnctionWegiveaproofofthestrongconvergenceinofthesolutionoftheparabolicapproximationtowardstheentropicsolutiontothescalarconservationlawwhereuo(RN),udenotessomeapproximationofuosuchthatandthefluxfsatisfiesTheconvergenceoftheapproximatesolutions...