正交表构造及其在数值计算的应用的Matlab实现

发布时间：2018-06-19 22:19

本文选题：正交表 + 区间收缩法　；参考：《河南师范大学》2017年硕士论文

【摘要】：本文首先根据已有的正交表的构造方法和原理并利用Matlab软件实现正交表的构造.比如利用哈达玛直积和特征函数生成N = 2s型正交表;利用正交拉丁方生成Lt2(tm)型正交表;再利用差集矩阵和向量内积分别生成Lλp2(pλp,+1)型和Lt4(tm)型正交表;最后利用并列法、递归构造分别生成混合水平正交表和高强度正交表.然后把非线性方程组和超定方程组的求解问题转化为函数极值的求解问题;再根据正交表区间收缩法求极值的思想,在一定的改进下,安排正交试验进而求得非线性方程组和超定方程组的解或者近似解.区间收缩法的优势在于不用通过求导就可以求得任何函数的极值点.这种方法解方程组,用时少,精确度高.特别地,矩阵是Matlab语言的基本的运算单元,所以使用Matlab运算矩阵有较大的优势.通常用C语言难以实现或者实现过程很复杂的,在Matlab中都能很容易的经过矩阵实现正交表的构造.本文主要研究了如何利用计算机快速生成正交表,及其在数值计算方面的应用.全文共分为四章:第一章介绍了全文的研究背景、相关概念和已有研究成果.第二章根据正交表的构造方法和原理,利用Matlab语言生成对称正交表、混合水平正交表和高强度正交表.第三章研究了如何在Matlab中利用区间收缩法将一类方程组的求解转化为函数求极值.第四章对本篇论文作出总结,并提出意见和建议.
[Abstract]:Firstly, according to the method and principle of orthogonal table, the orthogonal table is constructed by Matlab software. For example, using Hadamard direct product and characteristic function to generate N = 2s orthogonal table; using orthogonal Latin square to generate Lt2tm) type orthogonal table; then using difference set matrix and vector inner product to generate L 位 p2p 位 p, 1) and Lt4tm type orthogonal table respectively; finally, using parallel method, The mixed horizontal orthogonal table and the high intensity orthogonal table are constructed recursively. Then, the problem of solving nonlinear equations and overdetermined equations is transformed into the problem of solving the function extremum, and then according to the idea of finding the extreme value by the interval contraction method of orthogonal table, under certain improvement, The orthogonal test is arranged to obtain the solutions or approximate solutions of nonlinear equations and overdetermined equations. The advantage of interval contraction method is that the extremum of any function can be obtained without derivation. This method can solve equations with less time and high accuracy. In particular, the matrix is the basic operation unit of Matlab language, so the use of Matlab operational matrix has a great advantage. Usually the C language is difficult to implement or the process is very complex. In Matlab, it is easy to realize the construction of orthogonal table through matrix. This paper mainly studies how to quickly generate orthogonal table by computer and its application in numerical calculation. This paper is divided into four chapters: the first chapter introduces the research background, related concepts and existing research results. In the second chapter, according to the construction method and principle of orthogonal table, we use Matlab language to generate symmetric orthogonal table, mixed horizontal orthogonal table and high intensity orthogonal table. In the third chapter, we study how to use interval contraction method in Matlab to transform the solution of a class of equations into function to find the extremum. The fourth chapter summarizes this paper, and puts forward suggestions and suggestions.
【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.6

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