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man pages->IRIX man pages -> complib/QZIT (3)
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Contents

```
_QZIT(3F)							     _QZIT(3F)

```

NAME[Toc][Back]

```     QZIT, SQZIT  -  EISPACK routine.  This subroutine is the second step of
the QZ algorithm for solving generalized matrix eigenvalue	problems,

```

SYNOPSYS[Toc][Back]

```	  subroutine  qzit(nm, n, a, b,	eps1, matz, z, ierr)
integer	    nm,	n, ierr
double precision  eps1
double precision a(nm,n), b(nm,n), z(nm,n)
logical	   matz

subroutine sqzit(nm, n, a, b,	eps1, matz, z, ierr)
integer	    nm,	n, ierr
real		    eps1
real		   a(nm,n), b(nm,n), z(nm,n)
logical	   matz

```

DESCRIPTION[Toc][Back]

```     This subroutine accepts a pair of REAL matrices, one of them in upper
Hessenberg	form and the other in upper triangular form.  It reduces the
Hessenberg	matrix to quasi-triangular form	using orthogonal
transformations while maintaining the triangular form of the other
matrix.  It is usually preceded by	 QZHES	and followed by	 QZVAL	and,
possibly,	QZVEC.

On	Input

NM	must be	set to the row dimension of two-dimensional array parameters
as	declared in the	calling	program	dimension statement.

N is the order of the matrices.

A contains	a real upper Hessenberg	matrix.

B contains	a real upper triangular	matrix.

EPS1 is a tolerance used to determine negligible elements.	EPS1 = 0.0 (or
negative) may be input, in	which case an element will be neglected	only
if	it is less than	roundoff error times the norm of its matrix.  If the
input EPS1	is positive, then an element will be considered	negligible if
it	is less	than EPS1 times	the norm of its	matrix.	 A positive value of
EPS1 may result in	faster execution, but less accurate results.

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.

Z contains, if MATZ has been set to .TRUE., the transformation matrix
produced in the reduction by  QZHES, if performed,	or else	the identity

Page 1

_QZIT(3F)							     _QZIT(3F)

matrix.  If MATZ has been set to .FALSE., Z is not	referenced.  On	Output

A has been	reduced	to quasi-triangular form.  The elements	below the
first subdiagonal are still zero and no two consecutive subdiagonal
elements are nonzero.

B is still	in upper triangular form, although its elements	have been
altered.  The location B(N,1) is used to store EPS1 times the norm	of B
for later use by  QZVAL  and  QZVEC.

Z contains	the product of the right hand transformations (for both	steps)
if	MATZ has been set to .TRUE.

IERR is set to ZERO       for normal return, J	     if	neither
A(J,J-1) nor A(J-1,J-2) has become
zero after a total of 30*N iterations.	Questions and comments should
be	directed to B. S. Garbow, APPLIED MATHEMATICS DIVISION,	ARGONNE
NATIONAL LABORATORY

PPPPaaaaggggeeee 2222```
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