区间上一类连续自映射的单调迭代根

设Ｉ＝［０,１］,０＜ａ＜ｂ＜１,记Φ_ab≡｛Ｆ∈Ｃ^０（Ｉ）：Ｆ｜［０,ａ］和Ｆ｜［ｂ,１］严格单调递增且Ｆ在［ａ,ｂ］恒取常值｝．本文讨论了Ｆ∈Φ_ab有单调迭代根的充要条件．     

双对称非负定阵一类逆特征值问题的最小二乘解

１．引言 逆特征值问题在工程中有广泛的应用,其研究已有一些很好的结果［１－５］．最近,文［６］还研究了双对称矩阵逆特征值问题,即研究了如下两个问题： 问题Ａ．已知Ｘ∈Ｒｎｘｍ,Ａ＝ｄｉａｇ（λ１…,λｍ）,求Ａ∈ＢＳＲｎｘｎ使 ＡＸ＝ＸＡ,其中 Ｒｎｘｍ表示全体 ｎ ｘ ｍ实矩阵集合, ＢＳＲｎｘｎ表示全体 ｎ ｘ ｎ双对称阵集合． 问题Ｂ．已知Ａ＊ＥＲｎｘｎ,求Ａ∈ＳＥ使 ｜｜Ａ＊－Ａ｜｜＝ ｉｎｆ ｜｜Ａ＊－Ａ｜｜ ＡＦＳＥ其中 ＳＥ是问题 Ａ的解集合,｜｜． ｜｜表示 Ｆｒｏｂｅｎｉｕｓ范数． 在实际问题中, …     

逐次有理L_2逼近

逐次有理Ｌ_２逼近潘杰（合肥工业大学）ＳＵＣＣＥＳＳＩＶＥＲＡＴＩＯＮＡＬＬ＿２－ＡＰＰＲＯＸＩＭＡＴＩＯＮ￥ＰａｎＪｉｅ（ＨｅｆｅｉＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ）Ａｂｓｔｒａｃｔ：Ｌｅｔｆｕｎｃｔｉｏｎｆ∈Ｌ２［ａ，ｂ］，ｒａｔｉｏ?..     

关于奇异方程解的研究

本文用克莱姆法则，给出奇异方程ＡＸ＝ｂ［Ｉｎｄ（Ａ）＝ｋ，ｂ∈Ｒ（Ａｋ）］的唯一解，且如果Ａ是非奇异，可归纳到通常的克莱姆法则     

小议变上限的定积分

设函数ｆ（ｘ）在［ａ，ｂ］上可积，则对任何ｘ∈［ａ，ｂ］，定积分∫ｘａｆ（ｔ）ｄｔ定义了区间［ａ，ｂ］上的一个关于ｘ的函数Ｆ（ｘ），称为“变上限的定积分”，即Ｆ（ｘ）＝∫ｘａｆ（ｔ）ｄｔ，且若函数ｆ（ｘ）在［ａ，ｂ］上连续，则ｄｄｘ∫ｘａｆ（ｔ）ｄｔ...     

最佳L_P逼近对P的依赖性

设。本文证明了Ｎ（ｐ）（ｐ≥２）是Ｐ的可微函数，并且Ｎ（ｐ）在区间［１，∞］上满足Ｌｉｐｓｃｈｉｔｚ条件。设是定义在区间［ａ，ｂ］上的ｎ个线性无关的连续函数，记给定ｆ∈Ｌ∞［ａ，ｂ］，令Ｎ（ｐ）＝我们称ｖｐ（１≤Ｐ≤∞）是ｆ的最佳Ｌｐ逼近。     

关于阶数为奇数的布尔矩阵行空间的基数

设Ｂｎ表示所有的ｎ阶布尔矩阵的集合，Ｒ（Ａ）表示Ａ∈Ｂｎ的行空间，｜Ｒ（Ａ）｜表示Ｒ（Ａ）的基数．设ｍ，ｎ为正整数，本文证明了（Ⅰ）ｍ∈［１，４６］，［１，７８］，分别存在Ａ∈Ｂ７，Ａ∈Ｂ８，使得｜Ｒ（Ａ）｜＝ｍ．（Ⅱ）当ｎ≥９为奇数时，则ｍ∈［１，２（ｎ＋３）／２＋２（ｎ＋１）／２＋…＋２３］，存在Ａ∈Ｂｎ，使得｜Ｒ（Ａ）｜＝ｍ．     

关于半格的一个定理

文中给出了如下定理：设（Ｌ，∨，∧，Π，Σ），ＡＬ，则（Ａ，∨，∧，Σ）＝（Ａ，∨，∧，Π，Σ）ｉｆｆ（Ｌ，∧）上的内部算子Ｉ，使得Ａ＝｛ｘ：Ｉ（ｘ）＝ｘ｝＝ｒａｎｇｅ（Ｉ）＆ＢＡ，Ｉ∧ｂ∈Ｂｂ＝∧ｂ∈ＢＩ（ｂ）．另外，还给出［１］中定理１的一个改进证明．     

Notes on Oscillation of Solution for aCertain Second Order Neutral Equation

Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｃｏｎｓｉｄｅｒｏｓｃｉｌｌａｔｏｒｙｏｆｅｑｕａｔｉｏｎ（１）［ｘ（ｔ）＋ｃｘ（ｔ－τ）］″＋∫ｂａｐ（ｔ，ξ）ｘ［ｇ（ｔ，ξ）］ｄσ（ξ）＝０，（１）ｗｈｅｒｅτ０；ｐ（ｔ，ξ），ｇ（ｔ，ξ）∈Ｃ（［ｔ０，＋∞）×［ａ，ｂ］，Ｒ）；ｇ（ｔ，ξ）ｔ，ξ∈［ａ，ｂ］；ｇ（ｔ，ξ）ａｒｅｎｏｎ－ｄｅｃｒｅａｓｉｎｇｗｉｔｈｔｏｔ，ξ，ｒｅｓｐｅｃｔｉｖｅｌｙａｎｄｌｉｍｔ→＋∞ｍｉｎξ∈［ａ，ｂ］｛ｇ（ｔ，ξ）｝＝＋∞，σ（ξ）∈（［ａ，ｂ］，Ｒ）ｉｓｎｏｎｄｅｃｒ…     

一类无理函数最大值、最小值的求法

一类无理函数最大值、最小值的求法何国梁（湖南师大数学系４１０００６）由于对任意的ｔ∈［０，１］，都可通过代换ｘ＝（ｂ－ａ）ｔ＋ａ使得。ｘ∈［ａ，ｂ］，故在求形如的无理函数的最大值、最小值时，可先用换元的方法，换元后的函数的定义域成为［０，１］再利用三...     

Convergence of SSOR multisplitting method for an -matrix

In this paper, we study the convergence of both the multisplitting method and the relaxed multisplitting method associated with SSOR multisplitting for solving a linear system whose coefficient matrix is an H-matrix. We also introduce an application of the SSOR multisplitting method.     

关于对称正定矩阵的两级多分裂方法

为了在并行和向量机上求解对称正定性方程且Ax=b，两组多分裂方法被考虑，中，把Galligain和Ruggiero的两级算术平均方法推广到两级多分裂方法并给出了一些合适的内分裂例子，同时讨论了所引起的两级多分裂方法的收敛性。     

PARALLEL NONLINEAR MULTISPLITTING RELAXATION METHODS

ＰＡＲＡＬＬＥＬＮＯＮＬＩＮＥＡＲＭＵＬＴＩＳＰＬＩＴＴＩＮＧＲＥＬＡＸＡＴＩＯＮＭＥＴＨＯＤＳＷＡＮＧＤＥＲＥＮＡＮＤＢＡＩＺＨＯＮＧＺＨＩ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎ...     

并行区间矩阵多分裂AOR算法及其收敛性

本文提出了一类求解大型区间线性方程组的并行区间矩阵多分裂松弛算法,并在系数矩阵是区间H-矩阵的条件下,建立了这类算法的收敛理论。     

Convergence analysis of the parallel multisplitting TOR method

In this paper, we propose the parallel multisplitting TOR method, for solving a large nonsingular systems of linear equations Ax = b. These new methods are a generalization and an improvement of the relaxed parallel multisplitting method (Formmer and Mager, 1989) and parallel multisplitting AOR Algorithm (Wang Deren, 1991). The convergence theorem of this new algorithm is established under the condition that the coefficient matrix A of linear systems is an H-matrix. Some results also yield new convergence theorem for TOR method.     

PARALLEL CHAOTIC MULTISPLITTING ITERATIVE METHODS FOR THE LARGE SPARSE LINEAR COMPLEMENTARITY PROBLEM

1. IntroductionWe consider the linear complementarity problem LCP(M,q): Find a z E m such thatwhere M = (mij) E boxs and q ~ (qi) 6 m are given real matriX and vector, respectively.This problem axises in various scientific computing areas such as the Nash equilibritun poillt ofa bimatrir game (e.g., Cottle and Dantzig[4] and Lelnke[12j) and the free boundary problems offluid mechedcs (e.g., Cryer[8]). There have been a lot of researches on the approximate solutionof the linear complemeat…     

Multisection in Interval Branch-and-Bound Methods for Global Optimization – I. Theoretical Results

We have investigated variants of interval branch-and-bound algorithms for global optimization where the bisection step was substituted by the subdivision of the current, actual interval into many subintervals in a single iteration step. The convergence properties of the multisplitting methods, an important class of multisection procedures are investigated in detail. We also studied theoretically the convergence improvements caused by multisection on algorithms which involve the accelerating tests (like e.g. the monotonicity test). The results are published in two papers, the second one contains the numerical test result.     

Convergence of two-stage multisplitting method using AOR or SSOR multisplittings

In this paper, we study the convergence of two-stage multisplitting method using AOR or SSOR multisplittings as inner splittings and an outer splitting for solving a linear system whose coefficient matrix is an H-matrix. We also introduce an application of the two-stage multisplitting method.     

Two-Step Modulus-Based Synchronous Multisplitting Iteration Methods for Linear Complementarity Problems

To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based synchronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an $H_+$-matrix, which improve the existing convergence theory. Numerical results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation.     

关于线性互补问题的模系矩阵分裂迭代方法

模系矩阵分裂迭代方法是求解大型稀疏线性互补问题的有效方法之一.本文的目标是归纳总结模系矩阵分裂迭代方法的最新发展和已有成果,主要内容包括相应的多分裂迭代方法, 二级多分裂迭代方法和两步多分裂迭代方法, 以及这些方法的收敛理论.