Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems  

作　　者：Chein-Shan Liu Jian-Hung Shen Chung-Lun Kuo Yung-Wei Chen 

机构地区：[1]Center of Excellence for Ocean Engineering,Taiwan Ocean University,Keelung,202301,Taiwan,China [2]Department of Marine Engineering,Taiwan Ocean University,Keelung,202301,Taiwan,China

出　　处：《Computer Modeling in Engineering & Sciences》2024年第5期1317-1335,共19页工程与科学中的计算机建模（英文）

基　　金：the National Science and Tech-nology Council,Taiwan for their financial support(Grant Number NSTC 111-2221-E-019-048).

摘　　要：This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.

关 键 词：Nonlinear eigenvalue problem quadratic eigenvalue problem two new merit functions golden section search algorithm fictitious time integration method 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]