Page 207 - Compact Numerical Methods For Computers

196 Compact numerical methods for computers
Example 15.1. Illustration of the variable metric algorithm 21

The following output from an IBM 370/168 operating in single precision (six
hexadecimal digits) was produced by a FORTRAN version of algorithm 21 as it
minimised the Rosenbrock banana-shaped valley function (Nash 1976)

using analytic derivatives. The starting point b =-1·2, b =1 was used.
1
2
# ITNS= 1 # EVALNS= 1 FUNCTION= 0.24199860E+02
# ITNS= 2 # EVALNS= 6 FUNCTION= 0.20226822E+02
# ITNS= 3 # EVALNS= 9 FUNCTION= 0.86069937E+01
# ITNS= 4 # EVALNS= 14 FUNCTION= 0.31230078E+01
# ITNS= 5 # EVALNS= 16 FUNCTION= 0.28306570E+01
# ITNS= 6 # EVALNS= 21 FUNCTION= 0.26346817E+01
# ITNS= 7 # EVALNS= 23 FUNCTION= 0.20069408E+01
# ITNS= 8 # EVALNS= 24 FUNCTION= 0.18900719E+01
# ITNS= 9 # EVALNS= 25 FUNCTION= 0.15198193E+01
# ITNS= 10 # EVALNS= 26 FUNCTION= 0.13677282E+01
# ITNS= 11 # EVALNS= 27 FUNCTION= 0.10138159E+01
# ITNS= 12 # EVALNS= 28 FUNCTION= 0.85555243E+00
# ITNS= 13 # EVALNS= 29 FUNCTION= 0.72980821E+00
# ITNS= 14 # EVALNS= 30 FUNCTION= 0.56827205E+00
# ITNS= 15 # EVALNS= 32 FUNCTION= 0.51492560E+00
# ITNS= 16 # EVALNS= 33 FUNCTION= 0.44735157E+00
# ITNS= 17 # EVALNS= 34 FUNCTION= 0.32320732E+00
# ITNS= 18 # EVALNS= 35 FUNCTION= 0.25737345E+00
# ITNS= 19 # EVALNS= 37 FUNCTION= 0.20997590E+00
# ITNS= 20 # EVALNS= 38 FUNCTION= 0.17693651E+00
# ITNS= 21 # EVALNS= 39 FUNCTION= 0.12203962E+00
# ITNS= 22 # EVALNS= 40 FUNCTION= 0.74170172E-01
# ITNS= 23 # EVALNS= 41 FUNCTION= 0.39149582E-01
# ITNS= 24 # EVALNS= 43 FUNCTION= 0.31218585E-01
# ITNS= 25 # EVALNS= 44 FUNCTION= 0.25947951E-01
# ITNS= 26 # EVALNS= 45 FUNCTION= 0.12625925E-01
# ITNS= 27 # EVALNS= 46 FUNCTION= 0.78500621E-02
# ITNS= 28 # EVALNS= 47 FUNCTION= 0.45955069E-02
# ITNS= 29 # EVALNS= 48 FUNCTION= 0.15429037E-02
# ITNS= 30 # EVALNS= 49 FUNCTION= 0.62955730E-03
# ITNS= 31 # EVALNS= 50 FUNCTION= 0.82553088E-04
# ITNS= 32 # EVALNS= 51 FUNCTION= 0.54429529E-05
# ITNS= 33 # EVALNS= 52 FUNCTION= 0.57958061E-07
# ITNS= 34 # EVALNS= 53 FUNCTION= 0.44057202E-10
# ITNS= 35 # EVALNS= 54 FUNCTION= 0.0
# ITNS= 35 # EVALNS= 54 FUNCTION= 0.0
B( 1)= 0.10000000E+01
B( 2)= 0.10000000E+01
# ITNS= 35 # EVALNS= 54 FUNCTION= 0.0