关键词： Convergence   Cutting Planes   Nonconvex Programming  

摘要： We discuss the convergence of cutting plane algorithms for a class of nonconvex programs called the Generalized Lattice Point Problems (GLPP). A set of sufficient conditions which guarantee finite convergence are presented. Although these conditions are usually difficult to enforce in a practical implementation, they do illustrate the various factors that must be involved in a convergent rudimentary cutting plane algorithm. A striking example of nonconvergence (in which no subsequence converges to a feasible solution, even when seemingly strong cutting planes are used), is presented to show the effect of neglecting one such factor. We give an application of our analysis to problems with multiple choice constraints and finally discuss a modification of cutting plane algorithms so as to make finite convergence more readily implementable.

关键词： 钻孔方位   象限   编制   测点   点(数学)   测斜数据   地质图   地质剖面图   水平投影长   投影长度   井深   钻井剖面   钻孔剖面   孔斜   钻孔弯曲   取样位置  

摘要： 利用弯曲和方位角偏离的钻孔编制地质剖面图时,以前多采用投影制图法,用投影制图将钻孔校正到剖面图上的真正位置,需经几次投影搬点,误差较大。我队改用数学计算法代替投影制图法编制钻孔剖面图。经几年实践,证明了这一方法具有精度高、速度快、易于掌握等优点。特作一介绍。

关键词： 简表   方位角   向量积   叉积   数学计算   产状   计算公式   大地坐标   图解法   数值分析  

摘要： 本文提出一种数学计算方法,用来代替三点图解法求岩(矿)层的产状要素.试算结果较其三点图解法有速度快、精度高的特点. 应用条件与计算公式本法与三点图解法应用条件基本相同.即1.三点必须在同一层面上,但不得在一条直线上;2.三点的坐标及标高均为已知:3.三点范围内必无褶皱

关键词： 保密机   美国   美军   美利坚合众国   北美洲   密码机   飞机   数字加密   数学算法   声码器   数据通信设备   多卜勒频移   话音通信   话音信息通信   受话器   耳机   数传机   飞行员   飞行人员   外军  

摘要： 一、概述1960年美国《航空周刊》7月号报道了安装在 B—70和 F—108型飞机上的一种机载式声码器,为地对空提供可靠而保密的远距离通信。报道说该机传输速率2000b/s,自称清晰度单字为90%,句子99%,话音压缩比为6∶1,使用三级管250只,二级管915只,机器重60磅(27公斤),体积1.3立方呎。1972年,我军在抗美援越战争中,从被击落的美国战略轰炸机 B—52残骸中发现该飞机装有 ky—28保密机,并在机上找到有关保密机的资料。

关键词： 68A05   (05C35   05C38   16A78   65F05   68E10   C.1.2[processor architectures]: multiple data stream architectures (multiprocessors)-systolic arrays   G. 1.0 [numerical analysis]: general - parallel algorithms   G. 1.3 [numerical analysis]: numerical linear algebra - matrix inversion   G. 2.2 [discrete mathematics]: graph theory - path problems   B.6.1 [logic design]:design styles - cellular arrays   B.7.1 [integrated circuits]   types and design styles - algorithms implemented in hardware   VLSI (very large scale integration)   algorithms   design   performance   Algebraic path problem   shortest paths   transitive closure   closed semirings   Gau?-Jordan elimination  

摘要： It is shown how the Gau?-Jordan Elimination algorithm for the Algebraic Path Problem can be implemented on a hexagonal systolic array of a quadratic number of simple processors in linear time. Special instances of this general algorithm include parallelizations of the Warshall-Floyd Algorithm, which computes the shortest distances in a graph or the transitive closure of a relation, and of the Gau?-Jordan Elimination algorithm for computing the inverse of a real matrix.

关键词： 65J15   47H17   47H07   Nonlinear algebraic equations   Convergence   Interval arithmetic   Symmetric single-step method  

摘要： Some real and interval algorithms for the numerical solution of a class of nonlinear algebraic equations are described. These algorithms are based upon the symmetric single-step [2] and Newton [10], [11], [8] methods. Convergence theorems and numerical results which illustrate the effectiveness of the algorithms are given.

ISBN: (纸本)9787030464132

关键词： Algebraic reconstruction   digital ray tracing   tomography   ultrasound  

摘要： In this paper we have discussed what appears to be a superior implementation of the Algebraic Reconstruction Technique (ART). The method is based on 1) simultaneous application of the error correction terms as computed by ART for all rays in a given projection; 2) longitudinal weighting of the correction terms back-distributed along the rays; and 3) using bilinear elements for discrete approximation to the ray integrals of a continuous image. Since this implementation generates a good reconstruction in only one iteration, it also appears to have a computational advantage over the more traditional implementation of ART. Potential applications of this implementation include image reconstruction in conjunction with ray tracing for ultrasound and microwave tomography in which the curved nature of the rays leads to a non-uniform ray density across the image.