dtzrzf example program

This example solves the linear least squares problems

\min_{x} {‖b_{j} - A x_{j}‖}_{2}, j = 1, 2

for the minimum norm solutions

x_{1}

and

x_{2}

, where

b_{j}

is the

j

th column of the matrix

B

A = (\begin{array}{r} - 0.09 & 0.14 & - 0.46 & 0.68 & 1.29 \\ - 1.56 & 0.20 & 0.29 & 1.09 & 0.51 \\ - 1.48 & - 0.43 & 0.89 & - 0.71 & - 0.96 \\ - 1.09 & 0.84 & 0.77 & 2.11 & - 1.27 \\ 0.08 & 0.55 & - 1.13 & 0.14 & 1.74 \\ - 1.59 & - 0.72 & 1.06 & 1.24 & 0.34 \end{array}) and B = (\begin{array}{r} 7.4 & 2.7 \\ 4.2 & - 3.0 \\ - 8.3 & - 9.6 \\ 1.8 & 1.1 \\ 8.6 & 4.0 \\ 2.1 & - 5.7 \end{array}) .

The solution is obtained by first obtaining a

Q R

factorization with column pivoting of the matrix

A

, and then the

R Z

factorization of the leading

k

k

part of

R

is computed, where

k

is the estimated rank of

A

. A tolerance of

0.01

is used to estimate the rank of

A

from the upper triangular factor,

R

Note that the block size (NB) of

64

assumed in this example is not realistic for such a small problem, but should be suitable for large problems.

Example program for dtzrzf