The
by
(
) complex upper trapezoidal matrix
given by
where
is an
by
upper triangular matrix and
is an
by
matrix, is factorized as
where
is also an
by
upper triangular matrix and
is an
by
unitary matrix.
Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999)
LAPACK Users' Guide (3rd Edition) SIAM, Philadelphia
http://www.netlib.org/lapack/lugThe computed factorization is the exact factorization of a nearby matrix
, where
and
is the
machine precision.
The real analogue of this routine is
F08BHF (DTZRZF).
This example solves the linear least squares problems
for the minimum norm solutions
and
, where
is the
th column of the matrix
,
and