Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 615069, 11 pages
doi:10.1155/2009/615069
Research Article

Inverse Eigenvalue Problem of Unitary Hessenberg Matrices

Chunhong Wu1 and Linzhang Lu1,2

1School of Mathematical Sciences, Guizhou Normal University, Xiamen 361005, China
2School of Mathematics and Computer Science, Xiamen University, Guiyang 550001, China

Received 19 June 2009; Revised 28 August 2009; Accepted 31 August 2009

Academic Editor: Binggen Zhang

Copyright © 2009 Chunhong Wu and Linzhang Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let H∈ℂn×n be an n×n unitary upper Hessenberg matrix whose subdiagonal elements are all positive, let Hk be the kth leading principal submatrix of H, and let H˜k be a modified submatrix of Hk. It is shown that when the minimal and maximal eigenvalues of H˜k (k=1,2,…,n) are known, H can be constructed uniquely and efficiently. Theoretic analysis, numerical algorithm, and a small example are given.