Page 64 - Compact Numerical Methods For Computers

Handling larger problems 53
the factors Q and R gives back the original matrix apart from very small errors
which are of the order of the machine precision multiplied by the magnitude of
the elements in question.

*RUN
TEST GIVENS - GIFT - ALG 3 DEC: 12 77
SIZE -- M= ? 3 N= ? 4
MTIN - INPUT M BY N MATRIX
ROW 1 : ? 1 ? 2 ? 3 ? 4
ROW 2 : ? 5 ? 6 ? 7 ? 8
ROW 3 : ? 9 ? 10 ? 11 ? 12

ORIGINAL A MATRIX
ROW 1 : 1 2 3 4
ROW 2 : 5 6 7 8
HOW 3 : 9 10 11 12
GIVENS TRIANGULARIZATION DEC: 12 77
Q MATRIX
ROW 1 : 1 0 0
ROW 2 : 0 1 0
ROW 3 : 0 0 1
J= 1 K= 2 A[J,J]= 1 A[K,J]= 5
A MATRIX
ROW 1 : 5.09902 6.27572 7.45242 8.62912
ROW 2 : -1.19209E-07 -.784466 -1.56893 -2.3534
ROW 3 : 9 10 11 12
Q MATRIX
ROW 1 : .196116 -.980581 0
ROW 2 : .980581 .l96116 0
ROW 3 : 0 0 1
J = 1 K= 3 A[J,J]= 5.09902 A[K,J]= 9
A MATRIX
ROW 1 : 10.3441 11.7942 13.2443 14.6944
ROW 2 : -1.19209E-07 -.784466 -1.56893 -2.3534
ROW 3 : 0 -.530862 -1.06172 -1.59258
Q MATRIX
ROW 1 : 9.66738E-02 -.980581 -.170634
ROW 2 : .483369 .196116 -.853168
ROW 3 : .870063 0 .492941
J= 2 K= 3 A[J,J]=-.784466 A[K,J]=-.530862
FINAL A MATRIX
ROW 1 : 10.3441 11.7942 13.2443 14.6944
ROW 2 : 9.87278E-08 .947208 1.89441 2.84162
ROW 3 : -6.68l09E-08 0 -9.53674E-07 -1.90735E-06

FINAL Q MATRIX
ROW 1 : 9.66738E-02 .907738 -.40825
ROW 2 : .483369 .315737 .816498
ROW 3 : .870063 .276269 -.4408249
RECOMBINATION
ROW 1 : 1 2.00001 3.00001 4.00001
ROW 2 : 5.00001 6.00002 7.00002 8.00002
ROW 3 : 9.00001 10 11 12