matlab 非線性方程數值解法,非線性方程組的幾種數值解法+matlab源代碼

摘要很多領域都有涉及到非線性方程組，例如天氣預報，石油地質勘探，電力系統計算等，甚至商業領域也有非線性優化問題，這些問題要從本質上解決就是求出非線性方程組的解.但是目前已知的數值解法并不完善，選擇不同的方法，有着不同的收斂速度和計算量，而收斂速度和計算量影響着計算效率，是以數值解法的研究十分重要.58513

本篇論文首先簡單介紹了非線性方程組的幾種經典數值解法，如Newton法、區間疊代法、不動點疊代法等，并通過幾個數值例子，對一些經典的疊代型數值解法在收斂速度、計算量等方面進行對比分析，得出這些算法的優缺點，并研究了Newton法的改進算法.然後研究了同倫延拓法，最後給出了基于單純形法的螢火蟲算法及改進遺傳算法來求解非線性方程組.

畢業論文關鍵詞：Newton法；區間疊代法；不動點疊代法；遺傳算法；延拓法

Abstract  Many fields related to nonlinear equations, for example, weather forecasts and even life in the field of business, petroleum geological exploration, computing power system also has non-linear optimization problems that solve nonlinear equations is obtained essentially from the solution. However, currently known numerical method is not perfect, choose different methods and have different convergence speed and calculation, and the convergence rate and calculate the amount of influence the calculation of efficiency, so the numerical solution of the research is very important.

This paper first introduces some classical numerical solution of nonlinear equations, such as the Newton method, interval iterative method, fixed point iteration method, and through several numerical examples, some of the classic iterative numerical solution convergence the speed, the amount of calculation and other aspects of comparative analysis, the advantages and disadvantages of these algorithms, and to study the improved algorithm Newton method. Then we study the homotopy continuation method. Finally, the algorithm based on firefly and improved simplex method of genetic algorithm to solve nonlinear equations.

Keywords:Newton method; interval iterative method; fixed point iterative method; genetic algorithm; continuation method

目錄

第一章 緒論1

1.1 選題背景和意義1

1.2 研究現狀1

1.3 本文研究的主要内容1

第二章 幾種疊代法的分析及改進2

2.1 牛頓型疊代法3

2.1.1 牛頓法簡介3

2.1.2 三種牛頓法的比較5

2.1.3 九階牛頓型疊代法12

2.2 區間疊代法簡介17

2.2.1 區間與區間運算定義17

2.2.2 區間運算17

2.2.3 區間向量18

2.2.4 區間疊代法18

2.3不動點疊代法19

2.4 疊代型數值解法小結21

2.4.1執行個體分析21

2.4.2總結22

第三章 同倫延拓法及延拓法23

3.1延拓法及同倫延拓法23

3.2 執行個體27