Page 169 - Compact Numerical Methods For Computers

158 Compact numerical methods for computers
F( 10 )= 22228.5
F( 15 )= 22174.2
SUCCESS
F( 22.5)= 22202.2
PARAMIN STEP= 2.15087
F( 17.1509 )= 22168.6
NEW K4=-1.78772
F( 15.3631 )= 22172.6
FAILURE
F( 17.5978 )= 22168.8
PARAMIN STEP= 7.44882E-02
F( 17.2253 )= 22168.6
NEW K4=-.018622
F( 17.2067 )= 22168.6
SUCCESS
F( 17.1788 )= 22168.6
PARAMIN STEP=-4.65551E-03
F( 17.2021 )= 22168.6
PARAMIN FAILS
NEW K4= 4.65551E-03
F( 172114 )= 22168.6
FAILURE
F( 17.2055 )= 22168.6
PARAMIN FAILS
NEW K4= 0
MIN AT 17.2067 = 22168.6
12 FN EVALS
STOP AT 0060
*

The effect of step length choice is possibly important. Therefore, consider the
following applications of algorithm 17 using a starting value of t = 10.

Step length Minimum at Function evaluations

1 17·2264 13
5 17·2067 12
10 17·2314 10
20 17·1774 11

The differences in the minima are due to the flatness of this particular function,
which may cause difficulties in deciding when the minimum has been located. By
way of comparison, a linear search based on the success-failure/inverse interpola-
tion sequence in algorithm 22 found the following minima starting from t = 10.

Step length Minimum at Function evaluations
1 17·2063 23
5 17·2207 23
10 17·2388 21
20 17·2531 24