The
m by
n (
m≤n) complex upper trapezoidal matrix
A given by
where
R1 is an
m by
m upper triangular matrix and
R2 is an
m by
n-m matrix, is factorized as
where
R is also an
m by
m upper triangular matrix and
Z is an
n by
n 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
A+E, where
and
ε 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
x1 and
x2, where
bj is the
jth column of the matrix
B,
and