非线性特征值问题的二次近似方法

THE QUADRATIC APPROXIMATION METHODS FOR SOLVING NONLINEAR EIGENVALUE PROBLEMS

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.

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.