| 非线性特征值问题的二次近似方法 |
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| 引用本文： | 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 |
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| 作者姓名： | 曹阳 戴华 |
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| 作者单位： | 南京航空航天大学数学系, 南京 210016 |
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| 基金项目： | 国家自然科学基金(No. 11071118)资助项目. |
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| 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.
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| 关 键 词： | 非线性特征值问题 逐次二次近似方法 Arnoldi方法 Jacobi-Davidson方法 |
| 收稿时间： | 2013-10-09; |
THE QUADRATIC APPROXIMATION METHODS FOR SOLVING NONLINEAR EIGENVALUE PROBLEMS |
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| Cao Yang,Dai Hua. THE QUADRATIC APPROXIMATION METHODS FOR SOLVING NONLINEAR EIGENVALUE PROBLEMS[J]. Mathematica Numerica Sinica, 2014, 36(4): 381-392 |
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| Authors: | Cao Yang Dai Hua |
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| Affiliation: | Dept. of Math., Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China |
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| 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. |
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| Keywords: | nonlinear eigenvalue problems successive quadratic approximation method Arnoldi methods Jacobi-Davidson methods |
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