 
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
