SVM在解非線性方程式的應用

The application of SVM in solving nonlinear equations

林雨鵷(Lin Yu-Yuan)

指導教授 ： 曾正男 ； 吳柏林

國立政治大學/理學院/應用數學系/碩士(2020年)

https://doi.org/10.6814/NCCU202001843

摘要

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。

關鍵字

非線性方程式 ； 支持向量機

並列摘要

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.

並列關鍵字

Nonlinear equations ； SVM

參考文獻

[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.

[2] D. D. Wall. The order of an iteration formula. Mathematics of Computation, 10(55):167–168, Jan 1956.

[3] J. H. Wegstein. Accelerating convergence of iterative processes. Communications of the ACM, 1(6):9–13, Jan 1958.

[4] 張榮興. VISUAL BASIC 數值解析與工程應用. 高立圖書, 2002.

[5] Charles Houston. Gutzler. An iterative method of Wegstein for solving simultaneous nonlinear equations, 1959.