A Geometric Nonlinear Conjugate Gradient Method for Stochastic Inverse Eigenvalue Problems

Zhi Zhao Hangzhou Dianzi University Xiao-Qing Jin University of Macau Zheng-Jian Bai Xiamen University

Numerical Linear Algebra mathscidoc:1801.26001

SIAM Journal on Numerical Analysis, 54, (4), 2015-2035, 2016.7
In this paper, we focus on the stochastic inverse eigenvalue problem of reconstructing a stochastic matrix from the prescribed spectrum. We directly reformulate the stochastic inverse eigenvalue problem as a constrained optimization problem over several matrix manifolds to minimize the distance between isospectral matrices and stochastic matrices. Then we propose a geometric Polak–Ribi`ere–Polyak-based nonlinear conjugate gradient method for solving the constrained optimization problem. The global convergence of the proposed method is established. Our method can also be extended to the stochastic inverse eigenvalue problem with prescribed entries. An extra advantage is that our models yield new isospectral flow methods. Finally, we report some numerical tests to illustrate the efficiency of the proposed method for solving the stochastic inverse eigenvalue problem and the case of prescribed entries.
inverse eigenvalue problem, stochastic matrix, geometric nonlinear conjugate gradient method, oblique manifold, isospectral flow method
[ Download ] [ 2018-01-03 19:10:18 uploaded by zhaozhi ] [ 871 downloads ] [ 0 comments ]
@inproceedings{zhi2016a,
  title={A Geometric Nonlinear Conjugate Gradient Method for Stochastic Inverse Eigenvalue Problems},
  author={Zhi Zhao, Xiao-Qing Jin, and Zheng-Jian Bai},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180103191018907876864},
  booktitle={SIAM Journal on Numerical Analysis},
  volume={54},
  number={4},
  pages={2015-2035},
  year={2016},
}
Zhi Zhao, Xiao-Qing Jin, and Zheng-Jian Bai. A Geometric Nonlinear Conjugate Gradient Method for Stochastic Inverse Eigenvalue Problems. 2016. Vol. 54. In SIAM Journal on Numerical Analysis. pp.2015-2035. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180103191018907876864.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved