1. 毕业设计（论文）的内容和要求

矩阵特征值问题是数值代数领域的重要分支之一,在许多工程计算和现代科学中都有广泛的应用。

因此,研究矩阵特征值的求解方法具有重要的理论意义及应用价值。

本文主要研究用优化方法求解矩阵的特征值。

2. 参考文献

1. Zhanwen Shi，Guanyu Yang，Yunhai Xiao. A limited memory BFGS algorithm for non-convex minimization with applications in matrix largest eigenvalue problem. Mathematical Methods of Operations Research, 2016, 83 (2), 243#8211;264. 2.Andreas Stathopoulos.Nearly Optimal Preconditioned Methods for Hermitian Eigenproblems under Limited Memory. Part I: Seeking One Eigenvalue.2007,29(2),481-514. 3. Yuhong Dai. Unconstrained Optimization Models for Computing Several Extreme Eigenpairs of Real Symmetric Matrices. 4. CF Cui，YH Dai，J Nie. All Real Eigenvalues of Symmetric Tensors. Siam Journal on Matrix Analysis Applications, 2014, 35(4) 5. Andrew AL, Tan RCE. Iterative computation of derivatives of repeated eigenvalues and the corresponding eigenvectors. Numer Linear Algebra Appl ,2000, 7 : 151#8211;167. 6.Adhikari S, Friswell MI . Eigenderivative analysis of asymmetric non-conservative systems. Int J Numer Method Eng, 2000, 51:709#8211;733. 7.Mills-Curran WC . Calculation of eigenvector derivatives for structures with repeated eigenvalues. AIAA J, 1988, 26:867#8211;871. 8.Qian J, Andrew AL, Chu D, Tan RCE .Computing derivatives of repeated eigenvalues and corresponding eigenvectors of quadratic eigenvalue problems. SIAM J Matrix Anal Appl ,2013, 34:1089#8211;1111.

3. 毕业设计（论文）进程安排

1月-2月 确定选题，查找文献。

3月-4月上旬 论文的理论部分讨论。

4月中下旬 论文的数值计算的实现。