Page 168 - Compact Numerical Methods For Computers

One-dimensional problems 157

Simple grid search was applied to this function on Data General NOVA and
ECLIPSE computers operating in 23-bit binary and six-digit hexadecimal arithmetic,
respectively. The table at the bottom of the previous page gives the results of this
exercise. Note the difference in the computed function values!
An extended grid search (on the ECLIPSE) uses 26 function evaluations to
localise the minimum to within a tolerance of 0·1.

NEW
#
*ENTER SGRID #
*RUN
SGRID NOV 23 77
3 5 l978 16 44 31
ENTER SEARCH INTERVAL ENDPOINTS
AND TOLERANCE OF ANSWER’S PRECISION
? 10 ? 30 ? 1
ENTER THE NUMBER OF GRID DIVISIONS
F( 14 )= 22180.5
F( 18 )= 22169.2
F( 22 )=: 22195.9
F( 76 )= 22262.1
THE MINIMUM LIES IN THE INTERVAL. [ 14 , 22 ]
F( 15.6 )= 22171.6
F( 17.2 )= 22168.6
F( 18.8 )= 22171.6
F( 20.4 )=: 22180.7
THE MINIMUM LIES IN THE INTERVAL [ 15.6 , 18.8 ]
F( 16.24 )=: 22169.7
F( 16.88 )= 22168.7
F( 17.52 )= 22168.7
F( 18.16 )= 22169.7
THE MINIMUM LIES IN THE INTERVAL [ 16.24 , 17.52 ]
F( 16.496 )= 22169.2
F( 36.752 )= 22168.8
F( 17.008 ):= 22168.7
F( 17.264 )= 22168.6
THE MINIMUM LIES IN THE INTERVAL [ 17.008 , 17.52 ]
18 FUNCTION EVALUATIONS
NEW TOLERANCE ? .1
F( 17.1104 )= 22168.6
F( 17.2128 )= 22168.6
F( 17.3152 )= 22168.6
F( 17.4176 )= 22168.6
THE MINIMUM LIES IN THE INTERVAL [ 17.1104 , 17.3152 ]
F( 17.1513 )= 22168.6
F( l7.1923 )= 22168.6
F( 17.2332 )= 22168.6
F( 17.2742 )= 22168.6
THE: MINIMUM LIES IN THE INTERVAL [ 17.1923 , 17.2742 ]
26 FUNCTION EVALUATIONS
NEW TOLERANCE ? -1
STOP AT 0420
*
Algorithm 17 requires a starting point and a step length. The ECLIPSE gives

*
*RUN
NEWMIN JULY 7 77
STARTING VALUE= ? 10 STEP ? 5