二次項效應混合型牛頓疊代法之研究  二次項效應混合型牛頓疊代法之研究

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Title:	二次項效應混合型牛頓疊代法之研究二次項效應混合型牛頓疊代法之研究
Authors:	廖瑞聰;Ruey-Tsong Liaw
Contributors:	土木工程研究所
Keywords:	二次項效應混合型牛頓疊代法;非線性方程組疊代解法;數值分析;牛頓法;Numerical Method;Broyden’s method;Newton-Raphson method;mixed-type method
Date:	2001-06-27
Issue Date:	2009-09-18 17:08:42 (UTC+8)
Publisher:	國立中央大學圖書館
Abstract:	摘　要一般在工程上，遇到要處理非線性方程組時，大都採用牛頓－拉夫森法（Newton-Raphson method）來處理，但除了用牛頓－拉夫森法，其實有更多的有效率的方法可以來處理非線性方程組的問題。本研究的目的在於探討牛頓型迭代法加入二次項的效應配合牛頓－拉夫森法混合應用的混合型迭代法的探討；除了混合型迭代法的探討外，再介紹Broyden擬牛頓法(Broyden’s method)和共軛梯度法的應用和探討。以助於工程界在處理非線性方程組問題時，有更多元的選擇空間，做更有效率的處理。本研究將針對混合型迭代法，Broyden擬牛頓法和共軛梯度法對不同方程式進行一系列探討，主要探討內容為：（1）、各法迭代次數的比較。（2）、各法迭代cpu時間的比較。（3）、不同類型方程式對各法的改良比的比較。（4）、混合型迭代法切換參數的研究。 Abstract In general, most people deal with the nonlinear equations by the Newton-Raphson method. Besides the Newton-Raphson method，there are other effective methods can be used to solve the problems of nonlinear equations. The goal of this research is to investigate the method which takes the second order terms into the Newton-Raphson method. Besides research of the mixed-type method, Broyden’s method will alse be introduced to slove equations. This research will focus on the investigation between mixed-type method 、Broyden’s method and conjugate gradient method to different equations. The main issues are： 1. To study the numbers of iterations of each method. 2. To compare CPU time of iterations of each method. 3. The comparison of different kinds of equations treated by different methods. 4. The research on the mixed-type method for different switching parameters.
Appears in Collections:	[Graduate Institute of Civil Engineering] Electronic Thesis & Dissertation

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