Topic:On the power method for quaternion right eigenvalue problem
Speaker: Professor Wei Musheng
Event date: 3/22/2019
Event time: 9:30 a.m.
Venue: Lecture Hall 1508, Building 9
Sponsor: School of Mathematics and Statistics, Institute of Science and Technology
Brief Introduction of the Speaker:
Professor Wei Musheng, doctoral supervisor, belongs to Shanghai Normal University and is the distinguished professor of Liaocheng University. Professor Mu enjoys special allowance of the State Council and has won many national awards.
Abstract:
In this paper, we study the power method of the right eigenvalue problem of aquaternion matrix $A$. If $A$ is Hermitian, we propose the power method that is a direct generalization ofthat of complex Hermitian matrix. When $A$ isnon-Hermitian, by applyingthe properties of quaternion right eigenvalues, we propose the power method for computing the standard right eigenvalue with the maximum norm and the associated eigenvector. We also briefly discuss the inverse power method and shift inverse power method for the bothcases.The realstructure-preserving algorithm of the power method in the two cases is also proposed, and numerical examples are provided to illustrate the efficiency of the proposed power method and inverse power method.