 
Summary: An Efficient QR Algorithm for a Hessenberg
Submatrix of a Unitary Matrix
Gregory S. Ammar1
, William B. Gragg2
, and Chunyang He3
1
Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL
60115 USA. ammar@math.niu.edu
2
Department of Mathematics, Naval Postgraduate School, Monterey, CA 93943
USA. bill gragg@yahoo.com
3
Department of Mathematics and Statistics, University of MissouriKansas City,
5100 Rockhill Road, Kansas City, MO 641102499 USA.
chunyang@sbcglobal.net
Dedicated to Clyde Martin on the occasion of his sixtieth birthday.
Summary. We describe an efficient procedure for implementing the Hessenberg
QR algorithm on a class of matrices that we refer to as subunitary matrices. This
class includes the set of SzegoHessenberg matrices, whose characteristic polynomials
are Szego polynomials, i.e., polynomials orthogonal with respect to a measure on
