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| Title: | SVM在解非線性方程式的應用
The application of SVM in solving nonlinear equations |
| Authors: | 林雨鵷
Lin, Yu-Yuan |
| Contributors: | 曾正男
吳柏林
Zeng, Zheng-Nan
Wu, Bo-Lin
林雨鵷
Lin, Yu-Yuan |
| Keywords: | 非線性方程式
支持向量機
Nonlinear equations
SVM |
| Date: | 2020 |
| Issue Date: | 2021-01-04 11:09:49 (UTC+8) |
| Abstract: | 解非線性方程式雖然有許多數學標準方法，但是在高維度的求解以及有無窮多解的問題上，現有的方法可以計算出來的結果仍然非常有限，我們希望可以提出一個簡單快速的方法，可以了解無窮多解的分布狀況，並且在局部區域也能找出精確解，同時希望對這些解有可視化的了解。我們利用SVM的特性開發了一個新的方法，可以同時達到以上目標。
There are many standard mathematical methods for solving nonlinear equations. But when it comes to equations in high dimension with infinite solutions, the results from current methods are quite limited. We present a simple fast way which could tell the distribution of these infinite solutions and is capable of finding accurate approximations. In the same time, we also want to have a visual understanding about the roots. Using the features of SVM, we have developed a new method that achieves the above goals. |
| Reference: | [1] Bouchaib Radi and Abdelkhalak El Hami. Advanced Numerical Methods with Matlab 2 Resolution of Nonlinear, Differential and Partial Differential Equations. John Wiley & Sons, Incorporated, 2018.
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[7] G. Liu, C. Nie, and J. Lei. A novel iterative method for nonlinear equations. IAENG
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[9] G. Alefeld. On the convergence of halley’s method. The American Mathematical Monthly, 88(7):530, August 1981.
[10] George H. Brown. On halley’s variation of newton’s method. The American Mathematical Monthly, 84(9):726, November 1977.
[11] Yuri Levin and Adi BenIsrael. Directional newton methods in n variables. Mathematics of Computation, 71(237):251–263, May 2001.
[12] HengBin An and ZhongZhi Bai. Directional secant method for nonlinear equations. Journal of Computational and Applied Mathematics, 175(2):291–304, March 2005.
[13] HengBin An and ZhongZhi Bai. 關於多元非線性方程的broyden 方法. Mathematica Numerica Sinica, 26(4):385–400, November 2004. |
| Description: | 碩士
國立政治大學
應用數學系
107751015 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0107751015 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU202001843 |
| Appears in Collections: | [應用數學系] 學位論文
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