AOR方法的最优因子及效果分析

在[1]中提出了解线性代数方程组 A_x=b (1)的AOR方法: x~(m 1)=L_(α,ω)x~(m) ω(I-αL)~(-1)b, (2 L_(α,ω)=(I-αL)~(-1)[(1-ω)I (ω-α)L ωU], (3)其中A=I-L-U,L,U分别为严格下、上三角矩阵。AOR方法主要用于求解椭圆型离散化方程组,故上面可设diag(A)=I。现记B=L U。 当(2),(3)中两个参数取相同值时,AOR方法退化为相应参数的SOR方法。一个自然的问题是:能否在(2),(3)中选取适当的参数α,ω,使相应的AOR方法比最优参     

推广的迭代矩阵的收敛性

§1.引言 近若干年来,许多文献中讨论了线性代数方程组一些迭代格式的收敛性,亦即其系数矩阵A的各种分裂的收敛性和A为M阵或H阵的关系,例如Jacobi迭代、JOR迭代、SOR迭代、SSOR(对称SOR)迭代和AOR(快速SOR)迭代等等。在[4]中我们已将这样送代的迭代矩阵推广为 G_1=(D-RL)~(-1)[I-Ω)D (Ω-R)L ΩU], (1)这里D=diagA,L和U分别为-A的严格下三角矩阵和严格上三角矩阵,I为n阶单位阵,n为A的阶数,R和Ω为对角阵:     

某些迭代矩阵谱半径的上界估计

§1.引言在一些文献中对SOR、SSOR迭代矩阵的谱半径的上界进行了估计,例如对SOR的迭代矩阵■_w=(D—wL)~(-1)[(1—w)D wU] (1)的谱半径ρ(■_w)早有估计(例如[1]) ρ(■_w)≤|1-w| wρ(|J|),当0≤w≤2/(1 ρ(|J|))(2)此处设A为所考虑的线性代数方程组     

AOR迭代SOR迭代和JOR迭代的收敛性

1 引言和术语 已知n阶线性方程组 A_x=b, (1.1)其中A是n×n复或实矩阵,b是n维复或实向量。 本文研究当A是对角优势矩阵时,求解(1.1)的AOR迭代、SOR迭代和JOR迭     

AOR迭代法的收敛性

1.引言 [1]定义了解线性方程组A_x=b的AOR迭代法,它以SOR迭代为特例,而且适当选取参数,有可能比SOR方法收敛快(见[2]).众所周知,使 AOR方法有意义的最基本条件是A的对角元素都不为零.然而,在实际计算中,有时需要求解的线性方程组其系数矩阵存在零对角元素.例如[3]中研究的线性方程组的系数矩阵具有如下形式:     

关于ρ(L_(r,w))、ρ(J_w)的最小值

本文证明了当线性方程组系数矩阵 A之 Jacobi迭代矩阵 B=L+ U≥ 0 ,ρ( B) <1时 Gauss-Seidel法之迭代矩阵 G=L1,1的谱半径 ρ( G) =ρ( L1,1)是 ρ( Lr,w) ( 0≤ r≤w≤ 1 ,w>0 )中的最小值 ,即此时 Gauss-Seidel迭代是 AOR法中收敛最快的迭代法 .并且对 JOR法 (谱半径为 ρ( Jw) )和 SAOR法也作了相应的论述 .     

关于AOR迭代法的研究

本文论证了严格对角占优矩阵之AOR法的误差估计式中的误差估计常数hγ,ω（0≤γ≤ω0）的最小值是h1,1.     

一维p-Laplacian方程多点边值问题迭代解的存在性

运用Mawhin定理、上下解方法以及单调迭代技巧得到了下列具有p-Laplacian算子的多点边值问题{(φ_p(u′))′+f(t,u)=0,0≤t≤1,u(0)=0,u(1)=∑_(i=1)~(m-2)γ_iu(η_i)迭代解的存在性.进一步地,在允许f(t,u)变号的前提下,我们给出充分条件以保证解的非负性和非正性.     

Szàsz-Mirakian Kantorovich算子拟中插式的逼近等价定理

本文利用高阶光滑模ω■2r(f,t)p(1≤P≤∞)和ω■λ2r(f,t)∞(0≤λ≤1)得到了Szasz-Mirakian Kantorovich算子对于函数f∈Lp[0,00)(1≤P≤∞)的逼近等价定理.     

亚纯函数的级的估计

设f(z)为一亚纯函数,其级p< ∞。re~(iω_1),re~(iω_2),…,re~(iω_q)(r≥0)为q条射线,其中0≤ω_1<ω_2<…<ω_q<2π,q≥1。本文证明了若方程:f(z)=0,f(z)=∞,f~((l))(z)=1(l≥0,f~((0))≡f)的根均分布在包含上述q条射线的q个窄形区域中,又δ(0,f) δ(∞,f) δ(1,f~((l))>0,则     

Persistence and stability of solutions of Hamilton-Jacobi equations

Given a convergent sequence of Hamiltonians (Hn) and a convergent sequence of initial data (gn) for the first-order evolutionary Hamilton-Jacobi equation, we look for conditions ensuring that the sequences (un) and (vn) of Lax solutions and Hopf solutions respectively converge. The convergences we deal with are variational convergences. We take advantage of several recent results giving criteria for the continuity of usual operations.     

集值映射空间的收敛与邻近结构

S.Lubkin[1]对一个集合X定义邻近结构u,并把(X,u)称为空间。邻近结构是介于拓扑结构和一致结构之间的一种结构。本文将以作者在[6]中使用的集合间包含运算为工具,研究集值映射空间的邻近结构,以及刻划集值映射网的各种收敛的各种邻近结构。     

Cyrtologies of Convergences,I

We study the complete lattice of convergences, that is, of relations between a set and the set of its filters. Various properties of convergences (like isotonicity, antitonicity, being a pseudotopology, a pretopology, an adherence) determine subsets of the lattice of convergences which possess certain particular features called “cyrtological”. The morphisms associated to these sets, said “cyrtomorphisms”, are basic in the study of convergences. A method of generation of GALOIS connections relative to cyrtomorphisms is proposed. Semigroups generated by some cyrtomorphisms are analyzed.     

Some properties of bornological convergences

We study some basic properties of the so-called bornological convergences in the realm of quasi-uniform spaces. In particular, we revisit the results about when these convergences are topological by means of the use of pretopologies. This yields a presentation of the bornological convergences as a certain kind of hit-and-miss pretopologies. Furthermore, we characterize the precompactness and total boundedness of the natural quasi-uniformities associated to these convergences. We also obtain an extension of the classical result of Künzi and Ryser about the compactness of the topology generated by the Hausdorff quasi-uniformity to this framework.     

Convergences in JW-algebras and in their enveloping von Neumann algebras

We study properties of different convergences in JW-algebras with a faithful normal state. The relationship between these convergences and similar convergences in enveloping von Neumann algebras is established. Based on this, ergodic theorems are proved.     

On absolute, perfect, and unconditional convergences of double series in Banach spaces

We prove that, in the case of double series, perfect and unconditional convergences coincide, while absolute and perfect convergences do not coincide even for numerical series.     

直接最优化方法的收敛性与不动点

最优化方法中的直接法是仅仅利用目标函数值(或者通过试验结果)的信息,试图去寻求最优解.直接法迭代步骤简单,特别当目标函数的解析表达式十分复杂,甚至写不出来时,那些要求计算目标函数的偏导数的方法(称为解析方法)就无能为力了.然而,多因     

一类紧Fuzzy测度序列的淡收敛

经典测度的弱收敛和淡收敛在经典概率论等随机数学理论中有着很重要的作用。在局部紧Hausdorff空间中首次引入了一类紧Fuzzy 测度序列的淡收敛的概念,得到了它的等价形式及一些性质,推广了相应的经典结果。     

On Convergence of a Sequence of Parameterized Closed Convex Sets and Its Applications

Some abstract results about convergences for a sequence of parameterized nonempty closed convex sets, in the Mosco sense as well as in the sense of the local gap have been proved. By using these results, the convergences of some sequences of closed convex sets by certain general concrete structures arc discussed.     

Bornological Convergences on the Hyperspace of a Uniformizable Space

Bornological convergence is a generalization of the well known Attouch–Wets convergence. Our aim is to compare lower, upper and “two-sided” convergences generated by two compatible uniformities and two arbitrary bornologies. Moreover, the comparison of convergences induced by bounded-proximal topologies is characterized.