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非线性特征值问题的二次近似方法

曹阳, 戴华   

  1. 南京航空航天大学数学系, 南京 210016
  • 收稿日期:2013-10-09 出版日期:2014-11-15 发布日期:2014-12-06
  • 基金资助:

    国家自然科学基金(No. 11071118)资助项目.

曹阳, 戴华. 非线性特征值问题的二次近似方法[J]. 计算数学, 2014, 36(4): 381-392.

Cao Yang, Dai Hua. THE QUADRATIC APPROXIMATION METHODS FOR SOLVING NONLINEAR EIGENVALUE PROBLEMS[J]. Mathematica Numerica Sinica, 2014, 36(4): 381-392.

THE QUADRATIC APPROXIMATION METHODS FOR SOLVING NONLINEAR EIGENVALUE PROBLEMS

Cao Yang, Dai Hua   

  1. Dept. of Math., Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
  • Received:2013-10-09 Online:2014-11-15 Published:2014-12-06
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.

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