Nonnegative Inverse Eigenvalue and Singular Value Problems

Series: 
Applied and Computational Mathematics Seminar
Monday, February 16, 2015 - 14:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
National Chung Cheng University, Georgia Tech
,  
Organizer: 

Reference[1] Moody T. Chu

, Nonnegative Inverse Eigenvalue and Singular Value Problems, SIAM J. Numer. Anal (1992).[2] Wei Ma and Zheng-J. Bai, A regularized directional derivative-based Newton method for inverse singular value problems, Inverse Problems (2012).

Nonnegative inverse eigenvalue and singular value problems have been a research focus for decades. It is true that an inverse problem is trivial if the desired matrix is not restricted to any structure. This talk is to present two numerical procedures, based on a  conquering procedure and an alternating projection process, to solve inverse eigenvalue and singular value problems for nonnegative matrices, respectively.  In theory, we also discuss the existence of nonnegative matrices subject to prescribed eigenvalues and singular values.  Though the focus of this talk is on inverse eigenvalue and singular value problems with nonnegative entries, the entire procedure can be straightforwardly applied to other types of structure with no difficulty.