本文選題：正交表 + 區(qū)間收縮法　； 參考：《河南師范大學(xué)》2017年碩士論文

【摘要】：本文首先根據(jù)已有的正交表的構(gòu)造方法和原理并利用Matlab軟件實現(xiàn)正交表的構(gòu)造.比如利用哈達(dá)瑪直積和特征函數(shù)生成N = 2s型正交表;利用正交拉丁方生成Lt2(tm)型正交表;再利用差集矩陣和向量內(nèi)積分別生成Lλp2(pλp,+1)型和Lt4(tm)型正交表;最后利用并列法、遞歸構(gòu)造分別生成混合水平正交表和高強度正交表.然后把非線性方程組和超定方程組的求解問題轉(zhuǎn)化為函數(shù)極值的求解問題;再根據(jù)正交表區(qū)間收縮法求極值的思想,在一定的改進(jìn)下,安排正交試驗進(jìn)而求得非線性方程組和超定方程組的解或者近似解.區(qū)間收縮法的優(yōu)勢在于不用通過求導(dǎo)就可以求得任何函數(shù)的極值點.這種方法解方程組,用時少,精確度高.特別地,矩陣是Matlab語言的基本的運算單元,所以使用Matlab運算矩陣有較大的優(yōu)勢.通常用C語言難以實現(xiàn)或者實現(xiàn)過程很復(fù)雜的,在Matlab中都能很容易的經(jīng)過矩陣實現(xiàn)正交表的構(gòu)造.本文主要研究了如何利用計算機(jī)快速生成正交表,及其在數(shù)值計算方面的應(yīng)用.全文共分為四章:第一章介紹了全文的研究背景、相關(guān)概念和已有研究成果.第二章根據(jù)正交表的構(gòu)造方法和原理,利用Matlab語言生成對稱正交表、混合水平正交表和高強度正交表.第三章研究了如何在Matlab中利用區(qū)間收縮法將一類方程組的求解轉(zhuǎn)化為函數(shù)求極值.第四章對本篇論文作出總結(jié),并提出意見和建議.
[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.
【學(xué)位授予單位】：河南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.6

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