Please use this identifier to cite or link to this item: `https://ah.nccu.edu.tw/handle/140.119/133429`

 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-NanWu, Bo-Lin林雨鵷Lin, Yu-Yuan Keywords: 非線性方程式支持向量機Nonlinear equationsSVM 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.[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.[6] J.a. Ezquerro, A. Grau, M. GrauSánchez, M.a. Hernández, and M. Noguera. Analysing the efficiency of some modifications of the secant method. Computers & Mathematics with Applications, 64(6):2066–2073, 2012.[7] G. Liu, C. Nie, and J. Lei. A novel iterative method for nonlinear equations. IAENGInternational Journal of Applied Mathematics, 48:444–448, 01 2018.[8] Manoj Kumar, Akhilesh Kumar Singh, and Akanksha Srivastava. Various newtontype iterative methods for solving nonlinear equations. Journal of the Egyptian Mathematical Society, 21(3):334–339, October 2013.[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 Appears in Collections: [應用數學系] 學位論文

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