关键词： Conjugate Gradient   Constraint Violation   Previous Algorithm   Nonlinear Constraint   Mathematical Programming Problem  

摘要： In this paper, the problem of minimizing a function f(x) subject to a constraint φ{symbol}(x)=0 is considered, where f is a scalar, x an n-vector, and φ{symbol} a q-vector, with q s is such that φ{symbol}(x_s)=0, and at most N*=1+n -q if the starting point

摘要： Cids is an information storage and retrieval that performs on-line chemical structural searches. Among its retrieval screens are the atom-population of individual rings. This paper defines a class of rings for which screens are assigned and described briefly the algorithms by which computer programs analyze the structures for automatic screen assignment. The class of rings is independent of structure orientation, and may be defined equivalently as either the rings that are not the envelope of shorter rings or the rings that can be a member of a smaller set of smallest rings.

关键词： Algorithms   Management science   Simplex method   Nonlinear programming   Mathematical vectors   Optimal solutions   Working papers  

摘要： The problem manipulations and solution strategies of Part I of this paper are now further illustrated by combining them in various ways to yield several known algorithms. The main object is not an exposition of these algorithms, although this is certainly important; rather, we wish to focus on the principal patterns in which manipulations and strategies can be assembled. These patterns constitute the real common denominators in the literature on large-scale programming. See Table 2 in Part I.

关键词： FORMAC   FORTRAN   Navier-Stokes equations   continuity equation   curvilinear coordinate systems   symbolic manipulation   tensor   tensor equation  

摘要： A method is described whereby a digital computer can be used to derive the equations of mathematical physics in any curvilinear coordinate system requested by the user. The effectiveness of the technique is demonstrated by using it to derive the Navier-Stokes equations of fluid motion and the continuity equation. To derive these equations by this method, the user need know only the coordinate transformation equations relating the curvilinear coordinates of interest to an orthogonal Cartesian triad. When this program is used and the coordinate transformation equations are supplied as input, the computer will derive the Navier-Stokes equations and the continuity equation. The equations obtained will be relative to the curvilinear coordinate system specified by the transformation equations used as input. In this paper the emphasis is on theoretical considerations and methodology rather than on programming details. Results are presented for cylindrical polar and spherical polar coordinate systems. [ABSTRACT FROM AUTHOR]

摘要： A mathematical derivation of expected response time is presented for selected cyclic and priority scheduling disciplines, thereby demonstrating analytic techniques which may be utilized to evaluate such servicing doctrines. To illustrate the constant time quantum (round-robin) results, a hypothetical is defined and resolved.

摘要： No abstract available.

关键词： 代数学   近似算法  

摘要： 本通报1955年10月号發表了兩篇关於中等技术学校代数学教程中的近似算法的一些意見,看过后,我有一些不同的看法,願意提出来和大家共同研究。 (1)在通报的21頁最后所提到的是说:在原書(譯本)67頁例3中違背了近似数的乘法法則,我認为这正是符合於原書所提到的法則:在求中間結果时,应多取一个数字的法則是一致的。 (2)关於有效数字与存疑数字定义的問題,在胥長辰同志的意見認为应把这兩个定义統一起来,以避免兩个定义不相啣接,因此胥長辰同志認为应該修改,这样一来就忽視了近似数的最好的記法——四捨五入法,而这一方法在大綱中規定是中技校学生所必需掌握的,因此我認为除了原書所下的定义外,为了弥补这

关键词： 近似算法  

摘要： 作者在本文中举出(?)著,赵根榕、張理京译代數學教程第二章“近似算法”及第四章“幂舆根”中所存在的一些問题並提出了修改的意見,我們在这里特別指出作者在本文中所提出的準確有效數字的定義的修改意見与原書有着原则上的分歧,原書的定義是按四舍五入法的標准来确定一个近似数的有效數字的,四捨五入法是最好的近似数的記法,在中等技術學校里把計算和测量的结果按四捨五入法记錄下來這個規則介紹給學生對於养成學生的优良習慣來說是十分必要的。结合四捨五入法的規則來下準確有效數字的定義是有根据的。作者認為在實践中近似数可以採用四捨五入的記法,但在理論上準確有效数字不能以四捨五入的記法作為判斷的準繩,所以作者另下定義,這是和原書精神不一致的。 關於有效數字的定義,有規定以不超過近似数的最末位上半个單位為標準的(例如(?)的书),亦有規定以不超過最末一位上一个單位為標準的,也有兩種都採用的(例如(?)的近似计算法,但該書特别指出按四捨五入法記成的近似數,它的有效數字的定義是以下超過最末位上的半個單位為標準的)。闵乃大先生在近似數誤差分析(數學通報1954年10,11,12月號)一文則把符合第一種定義的数字稱為準確有效數字而把符合第二種定義的數字稱為可靠數字以示區別。究竟应該把那一種有效数字的定義介紹給中等技術學校的學生或者把兩種都介紹給學生的問题,我們希望有關讀者能展開討論,好有所决定。

关键词： 近似计算法   近似算法  

摘要： 最近教師們在使用中等技術學校代數學教程時,發現下面幾個問題: (1) 在第二章“近似算法”中,存疑數字的定義不够確印嚴密; (2) 準確有效數字和存疑數字的兩個定義不相啣接; (3) 在第四章開平方的近似算法中違反前面自己所立的法則(乘法); (4) 還違反了自己所立的四捨五入法 這樣就使教師們和同學們發生疑難,為了更好的學習蘇聯,讓我把該書的主要精神指出,並對錯誤部分提出一些補充和修正意見;還希望大家提供意見,來解决在使用教材中所發生的疑難問題。 (一) 該書關於“近似算法”的主要精神,在結合四捨五入法提出準確有效數字的定義 (1) 該書首先介紹數的四捨五入法(§19)這是最好的近似數的記法,測量值的記法是和四捨五入法一致的,也以誤差不超過最精細單位的