The Globally Optimal Iterative Algorithm with Critical Vector as a Descent Direction to Solve Algebraic Equations

• Main Authors: Chia-Jou Hsu, 徐佳柔
• Other Authors: Chein-Shan Liu
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/60106140795078106940

碩士 === 國立臺灣大學 === 土木工程學研究所 === 100 === It has always been of interest to solve algebraic equations used for describing physical and engineering issues. By using the concepts of the Steepest Descent method, the scalar homotopy method and the structure of light cone, we have developed a novel algorithm with preset parameters ϒ(0≤ϒ<1),ac (ac>1) and the critical parameter αc in the driving vector u=R+αcr and u=BTF+αcF as a descent direction. Due to the criticality of αc, we believe that by using this algorithm, the globally optimal solution can be obtained. It is so call the Globally Optimal Iterative Algorithm (GOIA). The GOIA has performed both great efficiency and accuracy when it is used for solving algebraic equations. Moreover, by using the GOIA, one can successfully avoid the calculation of the inverse Jacobian matrix which is required when use the Newton’s method instead.