共查询到20条相似文献,搜索用时 62 毫秒
1.
郭晓霞 《高等学校计算数学学报》1999,21(3):236-240
1引言一般的时离散代数Riccati方程具有下面的形式:这里如果方程(1)中的系数矩阵满足:(n=m)则方程(1)变为当Q=QT>0时,Engwerda,詹兴致等人研究了方程(2)存在正定解的充分必要条件[1][2][3].本章利用方程(2)与(1)的关系,从另一角度讨论了Q为对称矩阵时,方程(2)存在可稳定化解的充分必要条件.2基本概念与记号首先我们简单回顾一下以前的概念与记号.矩阵束M—N,M,N为正则的,也就是说det(λM-N)=0;如果λ0为det(λM-N)的k重根,则称λ0为它的k… 相似文献
2.
求解线性矩阵方程的初等变换法杨兴东(南京气象学院基科系,南京210044)杨兴洲(南京大学成人教育学院,南京210093)文[1]给出了线性矩阵方程AXB=C有解的简单判别法则,本文则应用初等变换,给出矩阵方程AXB=C(1)的简便解法.引理1[2]... 相似文献
3.
本文以两类非线性抛物型积分微分方程为例,首次尝试将插值后处理思想[1]应用到非线性发展型方程上,获得了半离散和全离散有限元解,经插值后处理之后在L∞(H1);L∞(L2)模意义下,整体超收敛1阶的高精度,并且计算量没有因此而增加.本文引进并证明较文[2]更广泛的一类椭圆H1-Volterra投影的H1;L2,H-1模最优估计.本文的分析方法可在各类发展型微分及积分微分方程上面通用. 相似文献
4.
1.引言解 Stiff ODEs初值问题的自开始型单块法已为 [4, 5]所研究.这里, e=(1,1,……,1)T为单位矩阵,当 时见 [4],当 0< a1< a2<…< ar= r时见[5]。 众所周知,解(1.1)的有效方法通常是隐的.仅当有效地解决了其变步长计算问题并具有有效的迭代法求其解时,这样的方法才能有效地用于实际计算.后者是不言而喻的,前者是由于定步长计算或者往往带来精度的严重损失,或者会带来计算量的严重增加(当存在(t0,T]的两个子区间,该两区间上的合理积分步长相差悬殊时,就会出现这种… 相似文献
5.
有理样条不可约解的行列式表示 总被引:3,自引:0,他引:3
1引言在文[1]中,对于剖分a=x0<x1<…<mn=b及给定的y0,y1,…, …,L+M-1,我们构造了有理样条S[L,M(x)Q[L,M]为次数不超过m的多项式全体.在[1]中,已经讨论了S[L,M](x)的存在性,并指出:若问题(1)(2)(3)可解,则解唯一这里总假设问题(1)(2)(3)可解.2有理样条解不可约的充要条件由S[L,M](x)的依区间递推算法(见[1]),我们只需讨论[x0,x1]上的情形.当[X0,x1]时,将S[L,M] (x),P[L,M] (x)和Q[L,M](… 相似文献
6.
7.
Toeplitz矩阵Tn=(ti-j)ni,j=0在信号处理、系统理论、逼近论、正交多项式、积分方程数值解等许多领域常常遇到.易知,Toeplitz矩阵Tn的逆矩阵一般不再是Toeplitz矩阵.1972年,Gohberg和Semencul[1]给出... 相似文献
8.
关于一种循环类预条件方程组的快速求解 总被引:3,自引:1,他引:2
1引言考虑下列N阶线性方程组其中C1=,C2=0≤i,j≤N-1,是N阶循环矩阵,J1=(J)是N阶置换矩阵,其元素分别满足1993年,T,K.Ku,C.C.J.Kuo在[1]中取C1,C2为实对称循环矩阵,而C1+J1C2作为预条件矩阵来求解在数字信号处理中有一定应用的Toeplitz加Hankel线性方程组[2],得到了一种高效的预处理其轭梯度算法.当Toeelitz与Hankel矩阵之和为正定矩阵且条件数适中时,所需运算量可达到0(Nlog2N),比原有算法[2,3,4]的运算量0(N2)… 相似文献
9.
Yang Lushan 《大学数学》1998,(2)
本文引入T(t)积分半群的概念,它是n次积分半群[1]及α次积分半群[2]的推广.我们给出T(t)积分半群的定义、生成定理,并讨论相应的一类积分型抽象Cauchy问题解的存在唯一性. 相似文献
10.
本文研究了任意体上的矩阵方程[X(nn)A(ns),X(nn)B(nt)]=[A(ns),0](1)给出了(1)相容的充要条件、通解的表达式、解的性质及其实用解法. 相似文献
11.
12.
ZHENG ShiJun 《分析论及其应用》2004,20(3)
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V. 相似文献
13.
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows 相似文献
14.
We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals. 相似文献
15.
Pankaj Mathur 《分析论及其应用》2006,22(2)
In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x). 相似文献
16.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary. 相似文献
17.
18.
《高校应用数学学报(英文版)》2014,29(4)
正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with 相似文献
19.
《数学研究及应用》2014,(6)
正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics. 相似文献
20.
A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6]. 相似文献