【摘要】 本文研究求解非线性特征值问题的数值方法.基于矩阵值函数的二次近似,将非线性特征值问题转化为二次特征值问题,提出了求解非线性特征值问题的逐次二次近似方法,分析了该方法的收敛性.结合求解二次特征值问题的Arnoldi方法和Jacobi-Davidson方法,给出求解非线性特征值问题的一些二次近似方法.数值结果表明本文所给算法是有效的.更多还原

【Abstract】 The numerical methods for solving nonlinear eigenvalue problems are considered in this paper.Based on the second-order approximation of matrix-valued functions,the nonlinear eigenvalue problems are transformed into the quadratic eigenvalue problems.A successive quadratic approximation method for solving the nonlinear eigenvalue problems is presented,and the convergence analysis of the method is given.Combining with Arnoldi and Jacobi-Davidson methods for solving the quadratic eigenvalue problems,some quadratic approximation methods for solving the nonlinear eigenvalue problems are given.Numerical results show that the proposed methods are efficient.更多还原