对称r-循环矩阵的快速算法和并行算法

借助于快速付立叶变换(FFT),给出了一种判断对称r-循环线性系统是否有解的快速算法,并且在有解的情况下求出其解,该算法的计算复杂度为O(nlogn),且具有很好的并行性,若使用n台处理机并行处理该算法则只需要O(logn)步.当r=0时,对称r-循环矩阵变成一个上三角型Hankel矩阵,我们也给出了此类矩阵求逆的一种算法.最后将该算法推广到线性同余系统,其运算量仅为O(nlogn).     

WDM网络中的一个改进的最优半光通道路由算法

本文在一个限定的条件下，提出了一个WDM网络中的寻找最优半光通道算法，使时间复杂度从O（k^2n km knlog(kn))提高到O（k^2n km nlogn)。     

多重三角T阵与多元多项式的快速除法

我们在[1]中给出了求三角形T矩阵的逆和计算一元多项式除法的O(nlogn)算法,改进了这两个问题已有的工作量为O(nlog~2n)的快速算法。本文给出了多重三角T阵的乘积、求逆和多元多项式的快速除法等快速方法,推广了[1]和[2]的结果。为叙述简便,我们仅就二重上三角形T阵与二元多项式除法讨论。由此不难推广到一般情形。     

关于多项式矩阵的快速除法

本文讨论了分块 T 型三角矩阵求逆和多项式矩阵除法的 O(k~2nlogn)快速算法,推广了文[3]的结果.     

离线k-服务器问题算法的改进

阐述了在k-服务器猜想的证明中改进经典的离线k-服务器问题算法的必要性,从而对经典算法进行了改进,设计了一种新算法,其复杂度由原来的O(m(nk)2)下降为O(mk2).     

基于核函数求解线性互补问题的不可行内点算法

本文研究了线性互补问题内点算法.利用全牛顿步长求解迭代方向,获得了算法迭代复杂性为O(nlogn/ε),推广了Roos等关于线性规划问题不可行内点算法,其复杂性与目前最好的不可行内点算法复杂性一致.     

基于全牛顿步长求解凸二次规划问题的不可行内点算法

借助于全牛顿步长对凸二次规划问题提出了一种新的不可行内点算法.算法主要迭代由可行迭代步和中心路径邻域迭代步组成.其优点是线性搜寻方向是不需要的.最后证明算法迭代复杂性为O(nlogn/ε),与目前最好的不可行内点算法复杂性一致.     

块Toeplitz三角阵求逆及块Toeplitz三角线性方程组求解的复杂性

In this paper, it is showed that the computational complexity of inversion of block triangular Toeplitz matrix U= (U₀, U₁,…, U_n-1 ) is O (m²nlogn + m³), as well as solution of block triangla r Toeplitz linear systems, where U 's are m×m mat rices. By using this results, we reduce arithmetic operations of division of polynomials from O(nlog²n) to O(nlogn).     

Computational Equivalence Between the Problems of Sorting and Monotone Reconstruction for Random Permutations

In this note,it is shown that the monotone reconstruction problem is equi-valent to that of sorting,in the sense of computational complexity.In particularfrom any given sorting al gorithm A,an algorithm B for the monotone reconstruc-tion problem can be developed with at most O(m)time and O(m)space cost morethan that used in A,and vice versa.As a consequence of this result,it is obtai-ned that the time complexity of the monotone reconstruction problem of n-ele-ment random perm utations is O(nlogn).     

关于多项式回归的复杂性界

多项式回归在回归分析方法中占有特别重要的地位.对具有N组测量数据的M次多项式回归问题,传统算法(例如用Householder变换)需O(N~2M)次算术运算。本文提出一种很简单的快速算法,该算法仅需O(NM)次算术运算。     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

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.     

CONTENTS OF VOLUME 30

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Instructions for contributions

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     

Journal of Mathematical Research with Applications Guide for Authors

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.     

Staircase transportation problems with superadditive rewards and cumulative capacities

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].     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.      

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Boundedness of multilinear operators on weighted herz type spaces

In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.     

THE EXACT CONVERGENCE RATE AT ZERO OF LAGRANGE INTERPOLATION POLYNOMIAL TO |x|α

In this paper we present a generalized quantitative version of a result due to M. Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f(x) = |x|α with on equally spaced nodes in [-1, 1].