Summary: Schur Flows for Orthogonal Hessenberg
Matrices \Lambda
Gregory S. Ammar y William B. Gragg z
Abstract
We consider a standard matrix flow on the set of unitary upper
Hessenberg matrices with nonnegative subdiagonal elements. The
Schur parametrization of this set of matrices leads to ordinary differ­
ential equations for the weights and the parameters that are analogous
with the Toda flow as identified with a flow on Jacobi matrices. We
derive explicit differential equations for the flow on the Schur param­
eters of orthogonal Hessenberg matrices. We also outline an efficient
procedure for computing the solution of Jacobi flows and Schur flows.
1 Introduction
Let H n denote the set of unitary upper Hessenberg matrices with nonnega­
tive subdiagonal elements. These matrices bear many similarities with real
\Lambda This version dated April, 1993. To appear in the Proceedings of the Fields Insti­
tute Workshop on Hamiltonian and Gradient Flows, Algorithms and Control, Waterloo,
Canada, March 29­31, 1992.
y Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115.
Internet: ammar@math.niu.edu. The work of this author was supported in part by the

Source: Ammar, Greg - Department of Mathematical Sciences, Northern Illinois University

Collections: Mathematics