关于变更的Adams-Moulton方法

§1.引言 1975年,Enright等人在[1]中通过各类典型的试验问题对常微分方程Stiff方程组的五个数值方法进行了数值比较,得到的结论之一是Enright方法很好.但也有弱点,即在使用它处理高度非线性Stiff系统时,与Gear方法和基于梯形公式的整体外插方法相比较,效果最差.其原因之一是对于任意一个Stiff系统来说,使用该方法在采用Newton-     

两类线性隐式方法

众所周知,在Stiff常微分方程组初值问题的数值解法中,向后微分公式(即Gear方法)是目前最通用的方法之一(见[1]).但是,Gear方法是一类隐式方法,在数值解的过程中,一般说来,每向前积分一步,需要解一个非线性方程组,它的求解是采用Newton-Raphson迭代方法,因此需要给出适当精度的预估值和计算右函数f(t,y)的Jacobi阵以     

一类求解Stiff微分方程的L-稳定显式单步法

近年来,由于Stiff微分方程在实践中的普遍性和重要性,对其数值解法的研究已经成为常微分方程的一项重点。 1975年,W.H.Enright,T.E.Hull和B.Lindberg著文,对现有求解Stiff方程的几种主要数值方法进行了全面的比较,在大量数值试验的基础上,初步结果表明,Gear的向后微分公式,Enright的二阶导数公式与Lindberg的梯形外推公式这三个方法     

一类含有稳定参数的Adams型隐式方法及其新算法

§1.引言 数值积分Stiff常微分方程初值问题,其积分过程的稳定性相当重要.用传统的数值方法,如Adams方法等,为保证计算稳定性,积分步长受到相当的限制.在stiff常微分方程初值问题的数值解法中,Gear方法是目前最通用的方法之一.但是,当阶p大     

一类k步k—1阶格式的研究

1.引言 基于数值微分的方法(或称Gear法)是当前处理Stiff问题的主导方法。该方法具有如下的形式: k y_(n 1)=sum from i=1 to k α_iy_(n 1-i) hβ_0f_(n 1)。 (1) 众所周知,当k≤6时,该方法是Stiff稳定的。积分过程所形成的隐式方程组必须用Newton-Raphson法求解,因为一般的简单迭代收敛性条件     

一类求解Stiff方程组显式单步法的改进

到目前为止,解Stiff常微分方程组的初值问题的绝大多数可行的数值方法都是隐式的,需要计算函数f(x,y)的Jacobi矩阵及与有关的某矩阵作LU分解。当m很大时,其计算量和存贮量都是惊人的。 针对上述困难,[1]、[2]和[3]中相继提出了一些L稳定的显式单步法。然而这些方法的精度及适用范围都受到一定限制且含有f的高阶全导数计算。本文针对Stiff方程组中同     

奇异摄动问题的二阶一致收敛指数型拟合差分格式

最近几年,许多人用各种方法研究奇异摄动问题的一致收敛数值方法(见[1]—[12]).作者将指数拟合Galerkin方法应用于Stiff两点边值问题,推导出简便的格式,并且在理论和实际计算上证明了此方法是二阶一致收敛的.     

三阶隐式线性三步方法的A_0-稳定和A(α)-稳定性

虽1引言 求解常微分方程初范间题 。夕,=八z,夕),z〔[z。,了’] 七y(l。)二多’。,,’,f“R,m)1的线性k步法具有形式 艺:,y二+,一h工刀,人十,·其中::+刀:,0产*,。.当刀、一。时,方法是显式的;否则,方法是稳式的. 当(1.1)是Stiff问题,特别是强Stiff问题时,通常考虑用隐式方法求解.1992年高等学校计算数学学报·1 59. 实践中常用的Adams一Moulton方法的稳定区域是复平而上的有限区域(k)2),因 此不适于求解Stiff间题.流行的Gear方法是双幻一稳定的,但是高阶方法:角比较小, 对于高振荡方程方法失效.针对这些问题,许多学者进行了研究,给出了…     

Neumann问题的渐近展开算法

一、问题的提出 Lions在[1]中引进的处理偏微分方程Stiff问题在变分形式中的渐近展开算法,多应用于含小参数0<ε<<1(在超导技术、低温物理和半导体技术中经常出现ε为10~(-21)量级的数.这时,ε比机器零还小,用通常的数值计算方法难以实施,只能应用渐近展开算法)的椭圆型方程齐次边值条件的Dirichlet问题.本文应用[1]的渐近展开方法和[2]中关     

一类A(α)-稳定降阶的Gear方法

<正>1引言线性多步法是求解常微分方程(组)的初值问题:{y'=f(x,y),a≤x≤b y(a)=y0的重要经典算法之一~([1-29]),其中具有A(α)-稳定性,可用于解刚性常微分方程的线性多步法的文献有:Gear于1968年在[9]中给出了一类Gear(BDF)方法;杨大地等于2008年在[17]中给出了一类YL方法,它的绝对稳定域比同阶Gear方法略大一些;Cash于1980年在[15]中给出了一种广义的向后差分方法;孙耿等于1981年在[20]中给出了一类变更的     

高阶非线性中立型方程正解的渐近性及存在性

本文利用非线性分析中半序方法和增算子不动点定理，对高阶非线性中立型方程正解的渐近性进行了详细分类，并且给出了各种类型正解存在的充要条件和具体例子．     

ASSESSMENT OF LOCAL INFLUENCE ONCOX'S PROPORTIONAL HAZARDS MODEL

1.IntroductionTheproportionalhazardsregressionmodelisasemiparametricmodel.Theloglikelihoodforthismodelisasumoverrisksets.Theperturbationofoneobservationedictsseveraloftheserisksets.Thus,theassessmentofcaseinfluenceismorecomplexforthismodelthanlinearandgeneralizedlinearmodels.TheglobalialluenceofindividualcaseonregressionparameterestimatesforCox'smodelhasbeenanalysedbyCainandLange[4],ReidandCrepeaull4],etal.TheideaofdtherentiationinsteadofdeletionisprominentinthelocalinduenceapproachofCook[…     

A theorem on tits geometries of type Cn

In this paper we extend a result of [2] to cover a more general situation. In [2] it was shown that a finite C_n geometry (n 4) in which all lines are thick and all C₃ residues are either buildings or flat has to be a building. Here we observe that the finiteness assumption of [2] was unnecessary in order to achieve the major part of the result. If we drop the finiteness assumption we can still prove that such a geometry is either a quotient of a building or flat. Flat C_n geometries for n 4 are seen to be degenerate in a certain sense. In the finite case with thick lines such degenerate geometries are easily shown not to exist, while finite buildings of type C_n with thick lines do not admit non-trivial quotients (Brouwer and Cohen, [1]). Thus the result of [2] follows as an immediate corollary of this more general case. The result does not hold when we drop the assumption that all lines are thick. In Section 3 we produce some examples of geometries of this type.     

A one parameter method for the matrix inverse square root

This paper is motivated by the paper [3], where an iterative method for the computation of a matrix inverse square root was considered. We suggest a generalization of the method in [3]. We give some sufficient conditions for the convergence of this method, and its numerical stabillity property is investigated. Numerical examples showing that sometimes our generalization converges faster than the methods in [3] are presented.     

Geometry of Multiplicity-Free Representations of GL(n), Visible Actions on Flag Varieties, and Triunity

We analyze the criterion of the multiplicity-free theorem of representations [5, 6] and explain its generalization. The criterion is given by means of geometric conditions on an equivariant holomorphic vector bundle, namely, the visibility of the action on a base space and the multiplicity-free property on a fiber.Then, several finite-dimensional examples are presented to illustrate the general multiplicity-free theorem, in particular, explaining that three multiplicity-free results stem readily from a single geometry in our framework. Furthermore, we prove that an elementary geometric result on Grassmann varieties and a small number of multiplicity-free results give rise to all the cases of multiplicity-free tensor product representations of GL(n,C), for which Stembridge [12] has recently classified by completely different and combinatorial methods.     

两种有效的非线性共轭梯度算法

根据CG-DESCENT算法[1]的结构和Powell在综述文献[11]中的建议,给出了两种新的求解无约束优化问题的非线性共轭梯度算法. 它们在任意线搜索下都具有充分下降性质, 并在标准Wolfe线搜索下对一般函数能够保证全局收敛性. 通过对CUTEr函数库中部分著名的函数进行试验, 并借助著名的Dolan & Moré[2]评价方法, 展示了新算法的有效性.     

Dealing with linear dependence during the iterations of the restarted block Lanczos methods

The Lanczos method can be generalized to block form to compute multiple eigenvalues without the need of any deflation techniques. The block Lanczos method reduces a general sparse symmetric matrix to a block tridiagonal matrix via a Gram–Schmidt process. During the iterations of the block Lanczos method an off-diagonal block of the block tridiagonal matrix may become singular, implying that the new set of Lanczos vectors are linearly dependent on the previously generated vectors. Unlike the single vector Lanczos method, this occurrence of linearly dependent vectors may not imply an invariant subspace has been computed. This difficulty of a singular off-diagonal block is easily overcome in non-restarted block Lanczos methods, see [12,30]. The same schemes applied in non-restarted block Lanczos methods can also be applied in restarted block Lanczos methods. This allows the largest possible subspace to be built before restarting. However, in some cases a modification of the restart vectors is required or a singular block will continue to reoccur. In this paper we examine the different schemes mentioned in [12,30] for overcoming a singular block for the restarted block Lanczos methods, namely the restarted method reported in [12] and the Implicitly Restarted Block Lanczos (IRBL) method developed by Baglama et al. [3]. Numerical examples are presented to illustrate the different strategies discussed.     

A ROBUST SUPERLINEARLY CONVERGENT ALGORITHM FOR LINEARLY CONSTRAINED OPTIMIZATION PROBLEMS UNDER DEGENERACY

1.IntroductionTheproblemconsideredinthispaperiswhereX={xER"laTx5hi,jEI={l,.'.,m}},ajeR"(jEI)areallcolumn*ThisresearchissupportedbytheNationalNaturalSciencesFoundationofChinaandNaturalSciencesFoundationofHunanProvince.vectors,hiERI(j6I)areallscalars,andf:R"-- Risacontinuouslydifferentiablefunction.Weonlyconsiderinequalityconstraintsheresinceanyequalitycanbeexpressedastwoinequalities.Withoutassumingregularityofthelinearconstraints,thereisnotanydifficultyinextendingtheresultstothegenera…     

Application of the method of partitioning the state of stress to the analysis of thermoelastic shells : PMM vol. 40, n 6, 1976, pp. 1085–1092

By using an asymptotic approach [1], the method of partitioning the state of stress is extended to thermoelastic shells. It is examined in detail in [2] forun-heated shells subjected to the effect of external forces, and consists of representing the total state of stress of the shell as the sum of those simpler states of stress for each of which the simplest methods for their construction can be given.Partitioning of the state of stress was performed in [3] for shells with a constant temperature over the thickness. It was noted in [4] in an analysis of a circular cylindrical shell by bending theory that integrals extended over the whole middle surface, which describe the fundamental state of stress, and integrals which damp out with distance from the edges and represent edge effects are contained in the general solution. In a number of papers, [5] for example, partitioning is performed on the basis of graphic physical representations for simple examples of analyzing circular cylindrical shells.A general approach to the analysis of rigid thermoelastic shells by the partitioning method is described below.     

Thomae formulae for general fully ramified <Emphasis Type="Italic">Z</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> curves

We generalize the elementary methods presented in several examples in the book [FZ] to obtain the Thomae formulae for general fully ramified Z _n curves.