EXACT BOUNDS OF THE MODIFIED LPT ALGORITHMS APPLYING TO PARALLEL MACHINES SCHEDULING WITH NONSIMULTANEOUS MACHINE AVAILABLE TIMES

ＥＸＡＣＴＢＯＵＮＤＳＯＦＴＨＥＭＯＤＩＦＩＥＤＬＰＴＡＬＧＯＲＩＴＨＭＳＡＰＰＬＹＩＮＧＴＯＰＡＲＡＬＬＥＬＭＡＣＨＩＮＥＳＳＣＨＥＤＵＬＩＮＧＷＩＴＨＮＯＮＳＩＭＵＬＴＡＮＥＯＵＳＭＡＣＨＩＮＥＡＶＡＩＬＡＢＬＥＴＩＭＥＳＬＩＮＧＵＯＨＵＩ，Ｈ...     

THE REAL CUBE DIFFERENTIAL SYSTEM WITH THREE REAL STRAIGHT LINE SOLUTIONS AND TWO CONJUGATE COMPLEX STRAIGHT LINE SOLUTIONS

ＴＨＥ　ＲＥＡＬ　ＣＵＢＥ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＳＹＳＴＥＭ　ＷＩＴＨ　ＴＨＲＥＥ　ＲＥＡＬ　ＳＴＲＡＩＧＨＴ　ＬＩＮＥ　ＳＯＬＵＴＩＯＮＳ　ＡＮＤ　ＴＷＯ　ＣＯＮＪＵＧＡＴＥ　ＣＯＭＰＬＥＸ　ＳＴＲＡＩＧＨＴ　ＬＩＮＥ　ＳＯＬＵＴＩＯＮＳＴＨ...     

ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR A CLASS OF THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATION

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＴＨＥＯＲＥＭＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＴＨＥＳＹＳＴＥＭＳＯＦＭＩＸＥＤＭＯＮＯＴＯＮＥＯＰＥＲＡＴＯＲＥＱＵＡＴＩＯＮＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＨＥＮＰＥＩＬＯＮＧ...     

THE GENERAL SCHEME FOR HIGHER－ORDER DECOMPOSITIONS OF ZERO－CURVATURE EQUATIONS ASSOCIATED WITH■（2）

ＴＨＥＧＥＮＥＲＡＬＳＣＨＥＭＥＦＯＲＨＩＧＨＥＲ－ＯＲＤＥＲＤＥＣＯＭＰＯＳＩＴＩＯＮＳＯＦＺＥＲＯ－ＣＵＲＶＡＴＵＲＥＥＱＵＡＴＩＯＮＳＡＳＳＯＣＩＡＴＥＤＷＩＴＨ■（２）￥ＺＥＮＧＹＵＮＢＯ（曾云波）（ＤｅｐｏｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａ...     

THERMODYNAMIQUE DES ENSEMBLES DE CANTOR AUTOSIMILAIRES（THERMODYNAMICS OF SELF-SIMILAR CANTOR SETS）

ＴＨＥＲＭＯＤＹＮＡＭＩＱＵＥＤＥＳＥＮＳＥＭＢＬＥＳＤＥＣＡＮＴＯＲＡＵＴＯＳＩＭＩＬＡＩＲＥＳ（ＴＨＥＲＭＯＤＹＮＡＭＩＣＳＯＦＳＥＬＦ－ＳＩＭＩＬＡＲＣＡＮＴＯＲＳＥＴＳ）￥Ｇ．ＭＩＣＨＯＮ;Ｊ．ＰＥＹＲＩＥＲＥ（ＵｎｉｖｅｒｓｉｔｙｄｅＢｏｕ...     

ANALYSES FOR A MATHEMATICAL MODEL OF THE PATTERN FORMATION ON SHELLS OF MOLLUSCS

ＡＮＡＬＹＳＥＳＦＯＲＡＭＡＴＨＥＭＡＴＩＣＡＬＭＯＤＥＬＯＦＴＨＥＰＡＴＴＥＲＮＦＯＲＭＡＴＩＯＮＯＮＳＨＥＬＬＳＯＦＭＯＬＬＵＳＣＳＭＥＩＭＩＮＧＡＮＤＸＩＡＯＹＩＮＧＫＵＮＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒａｎａｌｙｓｅｓａｍａｔｈｅｍａｔｉ...     

扩散系数反问题正则化数值方法的收敛性分析

扩散系数反问题正则化数值方法的收敛性分析朝红阳（中山大学计算机科学系）ＣＯＮＶＥＲＧＥＮＣＥＡＮＡＬＹＳＩＳＯＦＡＲＥＧＵＬＡＲＩＺＥＤＮＵＭＥＲＩＣＡＬＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＴＨＥＤＩＦＦＵＳＩＶＥＣＯＥＦＦＩＣＩＥＮＴＩＮＶＥＲＳＥＰＲ...     

THE DISCRETE DYNAMICS FOR COMPETITIVE POPULATIONS OF LOTKA-VOLTERRA TYPE

ＴＨＥＤＩＳＣＲＥＴＥＤＹＮＡＭＩＣＳＦＯＲＣＯＭＰＥＴＩＴＩＶＥＰＯＰＵＬＡＴＩＯＮＳＯＦＬＯＴＫＡ－ＶＯＬＴＥＲＲＡＴＹＰＥＬＩＵＬＡＩＦＵＡＮＤＧＯＮＧＢＩＮＡｂｓｔｒａｃｔ：Ｔｈｅｄｉｓｃｒｅｔｅｄｙｎａｍｉｃｓｆｏｒｃｏｍｐｅｔｉｔｉｏｎｐ...     

THE CONVERGENCE OF GLOWINSKI'S ALGORITHM FOR ELLIPTIC PROBLEMS

ＴＨＥＣＯＮＶＥＲＧＥＮＣＥＯＦＧＬＯＷＩＮＳＫＩ＇ＳＡＬＧＯＲＩＴＨＭＦＯＲＥＬＬＩＰＴＩＣＰＲＯＢＬＥＭＳＣＨＵＤＥＬＩＮ（储德林）；ＨＵＸＩＡＮＣＨＥＮＧ（胡显承）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｔｓｉｎｇ－Ｈｕ...     

OPTIMAL AND SUPERCONVERGENCE ESTIMATES OF THE FIMITE ELEMENT METHOD FOR A SCALAR HYPERBOLIC EQUATION

ＯＰＴＩＭＡＬＡＮＤＳＵＰＥＲＣＯＮＶＥＲＧＥＮＣＥＥＳＴＩＭＡＴＥＳＯＦＴＨＥＦＩＭＩＴＥＥＬＥＭＥＮＴＭＥＴＨＯＤＦＯＲＡＳＣＡＬＡＲＨＹＰＥＲＢＯＬＩＣＥＱＵＡＴＩＯＮＺｈｏｕＡｉｈｕｉ（周爱辉）ＬｉｎＱｕｎ（林群）（Ｉｎｓｔ．ｏｆＳｙｓ．Ｓｃ...     

研究伪随机数序列独立性的均匀偏度法

§1 引言 由具有在[0,1]上均匀分布的总体中产生的简单子样称为随机数序列,其中的每一样本称为随机数。所谓伪随机数序列,一般是指用数学递推公式所产生的随机数序列。如最常见的乘同余方法,它所产生的伪随机数序列就是对给定的正整数M和小于M的任意正整数初值β_1,用如下递推公式确定的:     

自适应多重网格法与超松弛法的比较

多重网格法(Multiple Grid Method,简称M-G方法)是近年来出现的快速方法之一,本文在M-G方法中采用自适应控制层间转换的技术,并将自适应M-G方法与G-S迭代方法及SOR迭代方,法进行了比较。其计算结果表明,自适应M-G方法的计算量比G-S迭代及SOR迭代少得多,当M-G方法所用层数为4-6层,这种优越性就更加明显,且自适应M-G方法中选取控制参数有很大的灵活性。     

A modified Hestenes–Stiefel projection method for constrained nonlinear equations and its linear convergence rate

The Hestenes–Stiefel (HS) method is an efficient method for solving large-scale unconstrained optimization problems. In this paper, we extend the HS method to solve constrained nonlinear equations, and propose a modified HS projection method, which combines the modified HS method proposed by Zhang et al. with the projection method developed by Solodov and Svaiter. Under some mild assumptions, we show that the new method is globally convergent with an Armijo line search. Moreover, the R-linear convergence rate of the new method is established. Some preliminary numerical results show that the new method is efficient even for large-scale constrained nonlinear equations.     

Finding roots of a real polynomial simultaneously by means of Bairstow's method

Aberth's method for finding the roots of a polynomial was shown to be robust. However, complex arithmetic is needed in this method even if the polynomial is real, because it starts with complex initial approximations. A novel method is proposed for real polynomials that does not require any complex arithmetic within iterations. It is based on the observation that Aberth's method is a systematic use of Newton's method. The analogous technique is then applied to Bairstow's procedure in the proposed method. As a result, the method needs half the computations per iteration than Aberth's method. Numerical experiments showed that the new method exhibited a competitive overall performance for the test polynomials.     

Accelerated Imaginary-time Evolution Methods for the Computation of Solitary Waves

Two accelerated imaginary-time evolution methods are proposed for the computation of solitary waves in arbitrary spatial dimensions. For the first method (with traditional power normalization), the convergence conditions as well as conditions for optimal accelerations are derived. In addition, it is shown that for nodeless solitary waves, this method converges if and only if the solitary wave is linearly stable. The second method is similar to the first method except that it uses a novel amplitude normalization. The performance of these methods is illustrated on various examples. It is found that while the first method is competitive with the Petviashvili method, the second method delivers much better performance than the first method and the Petviashvili method.     

A global convergent quasi-Newton method for systems of monotone equations

In this paper, we propose a quasi-Newton method for solving systems of monotone equations. The method is a combination of the Broyden method and the hyperplane projection method. Under appropriate conditions, we prove that the proposed method is globally convergent. Preliminary numerical results show that the proposed method is promising.     

一种求解非线性互补问题的方法及其收敛性

本文将Newton方法和外梯度方法相结合,提出了一种求解非线性互补问题的方法,证明了此方法的全局收敛性和超线性收敛性,在适当的条件下给出了一个有限终止结果。数值实验表明,此方法是有效的。     

求解病态线性方程组的收缩Lanczos方法

Lanczos方法是求解大型线性方程组的常用方法.遗憾的是,在Lanczos过程中通常会发生算法中断或数值不稳定的情况.将给出求解大型对称线性方程组的收缩Lanczos方法,即DLanczos方法.新算法将采用增广子空间技术,在Lanczos过程中向Krylov子空间加入少量绝对值较小的特征值所对应的特征向量进行收缩.数值实验表明,新算法比Lanczos方法收敛速度更快,并且适合求解病态对称线性方程组.     

A COLUMN-SECANT UPDATE TECHNIQUE FOR SOLVING SYSTEM OF NONLINEAR EQUATIONS

In this paper,we present a column-secant modification of the SCC method,which is called the CSSCC method.The CSSCC method uses function values more efficiently than the SCC method,and it is shown that the CSSCC method has better local q-convergence and r-convergence rates than the SCC method.The numerical results show that the CSSCC method is competitive with some well known methods for some standard test problems.     

拟Raabe判别法与拟对数判别法的强弱关系

拟Raabe判别法是新近提出的关于正项级数收敛性的一种比较细致的判别法.对通项递减的正项级数来说,此判别法强于传统的Raabe判别法与Gauss判别法.通过对拟Raabe判别法与另一个细致的判别法——拟对数判别法强弱关系的探讨,得出了后一判别法强于前者的结论.