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# qzhess

## PURPOSE

% Compute the Hessenberg-triangular decomposition of the matrix pencil

## SYNOPSIS

function [aa, bb, q, z] = qzhess (a, b)

## DESCRIPTION

```% -*- texinfo -*-
% @deftypefn {Function File} {[@var{aa}, @var{bb}, @var{q}, @var{z}] =} qzhess (@var{a}, @var{b})
% Compute the Hessenberg-triangular decomposition of the matrix pencil
% @code{(@var{a}, @var{b})}, returning
% @code{@var{aa} = @var{q} * @var{a} * @var{z}},
% @code{@var{bb} = @var{q} * @var{b} * @var{z}}, with @var{q} and @var{z}
% orthogonal.  For example,
%
% @example
% @group
% [aa, bb, q, z] = qzhess ([1, 2; 3, 4], [5, 6; 7, 8])
%      @result{} aa = [ -3.02244, -4.41741;  0.92998,  0.69749 ]
%      @result{} bb = [ -8.60233, -9.99730;  0.00000, -0.23250 ]
%      @result{}  q = [ -0.58124, -0.81373; -0.81373,  0.58124 ]
%      @result{}  z = [ 1, 0; 0, 1 ]
% @end group
% @end example
%
% The Hessenberg-triangular decomposition is the first step in
% Moler and Stewart's QZ decomposition algorithm.
%
% Algorithm taken from Golub and Van Loan, @cite{Matrix Computations, 2nd
% edition}.
% @end deftypefn```

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:

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