國立臺南大學應用數學系

Speaker：Matthew M. Lin (Department of Mathematics, National Cheng Kung University)

Title: A Riemannian Inexact Newton-CG Method for Inverse Eigenvalue and
Singular Value Problems

Abstract: 
Inverse eigenvalue and singular value problems have been widely discussed
for decades. 
The well-known result is the Weyl-Horn condition, which presents the
relations between the eigenvalues and singular values of an arbitrary
matrix. This result by Weyl-Horn then leads to an interesting inverse
problem, i.e., how to construct a matrix with desired eigenvalues and
singular values. In this talk, two topics will be included. First, we
provide a necessary and sufficient condition for the existence of a 2-by-2
real matrix, or even a nonnegative matrix, with prescribed eigenvalues,
singular values, and main diagonal entries. Second, we propose an eclectic
mix of techniques from differential geometry and the inexact Newton method
for solving inverse eigenvalue and singular value problems as well as
additional desired characteristics such as nonnegative entries, prescribed
diagonal entries, and even predetermined entries. We show theoretically that
our method converges globally and quadratically, and we provide numerical
examples to demonstrate the robustness and accuracy of our proposed method.

Time : 11/7(三)  PM 2:00-4:00

Place: Gezhi Science Hall C305 Department of Applied Mathematics, National University of Tainan