QZHES(3)

SYNOPSIS
SUBROUTINE QZHES (NM, N, A, B, MATZ, Z)

NAME
qzhes - The first step of the QZ algorithm for solving generalized matrix eigenproblems. Accepts a pair of real general matrices and reduces one of them to upper Hessenberg and the other to upper triangular form using orthogonal transformations. Usually followed by QZIT, QZVAL, QZVEC.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C1B3

TYPE
SINGLE PRECISION (QZHES-S)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is the first step of the QZ algorithm for solving generalized matrix eigenvalue problems, SIAM J. NUMER. ANAL. 10, 241-256(1973) by MOLER and STEWART. This subroutine accepts a pair of REAL GENERAL matrices and reduces one of them to upper Hessenberg form and the other to upper triangular form using orthogonal transformations. It is usually followed by QZIT, QZVAL and, possibly, QZVEC. On Input NM must be set to the row dimension of the two-dimensional array parameters, A, B, and Z, as declared in the calling program dimension statement. NM is an INTEGER variable. N is the order of the matrices A and B. N is an INTEGER variable. N must be less than or equal to NM. A contains a real general matrix. A is a two-dimensional REAL array, dimensioned A(NM,N). B contains a real general matrix. B is a two-dimensional REAL array, dimensioned B(NM,N). MATZ should be set to .TRUE. if the right hand transformations are to be accumulated for later use in computing eigenvectors, and to .FALSE. otherwise. MATZ is a LOGICAL variable. On Output A has been reduced to upper Hessenberg form. The elements below the first subdiagonal have been set to zero. B has been reduced to upper triangular form. The elements below the main diagonal have been set to zero. Z contains the product of the right hand transformations if MATZ has been set to .TRUE. Otherwise, Z is not referenced. Z is a two-dimensional REAL array, dimensioned Z(NM,N). Questions and comments should be directed to B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY ------------------------------------------------------------------

REFERENCES
B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen- system Routines - EISPACK Guide, Springer-Verlag, 1976.

ROUTINES CALLED
(NONE)

REVISION HISTORY (YYMMDD)
760101 DATE WRITTEN
890831 Modified array declarations. (WRB)
890831 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
920501 Reformatted the REFERENCES section. (WRB)