Page 217 - Compact Numerical Methods For Computers

206 Compact numerical methods for computers
2 31 5.76718E-04
3 31 5.76718E-04
4 42 5.76716E-04
5 42 5.76716E-04
6 45 5.76713E-04
7 45 5.76713E-04
8 48 5.76711E-04
9 48 5.76711E-04
CONVERGED TO 5.76711E-04 # lTNS= 10 # EVALS= 50
# EFES= 290
B( 1 )= 167.85 G( 1 )= .148611
B( 2 )= .900395 G( 2 )= 194.637
B( 3 )= 167.85 G( 3 )= .148611
B( 4 )= .900721 G( 4 )= 206.407
B( 5 )=-99.69 G( 5 )= .148626
B( 6 )= 167.85 G( 6 )= .145611
B( 7 )= .900675 G( 7 )= 204.746
B( 8 )=-74.33 G( 8 )= .148626
B( 9 )= 167.85 G( 9 )= .148611
B( 10 )= .900153 G( 10 )= 185.92
B( 11 )=-4.79994 G( 11 )= 2.22923
B( 12 )=-1.02951 G( 12 )= 17.7145
B( 13 )=-.999114 G( 13 )= 31.9523
B( 14 )= 3.42012 G( 14 )= 4.42516
B( 15 )=-65.1549 G( 15 )= 2.22924
B( 16 )=-.726679 G( 16 )= 119.818
B( 17 )=-.114509 G( 17 )= 157.255
B( 19 )=-20.8499 G( 18 )= 3.5103
B( 19 )= 1.21137 G( 19 )= 410.326
B( 20 )=-2.84145 G( 20 )= 308.376
B( 21 )= 31.6001 G( 21 )= 4.42516
B( 22 )=-20.6598 G( 22 )= 4.36376
B( 23 )=-8.54979 G( 23 )= 7.66536
STOP AT 0911
*SIZE
USED: 3626 BYTES
LEFT: 5760 BYTES
*

An earlier solution to this problem, obtained using a Data General NOVA
operating in 23 binary digit arithmetic, had identical values for the parameters B
but quite different values for the gradient components G. The convergence
pattern of the program was also slightly different and had the following form:

0 1 772741
1 21 5.59179E-4
2 22 5.59179E-4
CONVERGED TO 5.59179E-4 # ITNS= 3 # EVALS= 29

In the above output, the quantities printed are the number of iterations
(gradient evaluations), the number of function evaluations and the lowest function
value found so far. The sensitivity of the gradient and the convergence pattern to
relatively small changes in arithmetic is, in my experience, quite common for
algorithms of this type.