Simplex Optimization
12)
Silver.G.L..in "Mound Facilitv Aetivitiesin Chemical and Phvsiaal Research: Julr-
To the Editor:
The September, 1983, edition of THIS JOURNAL contains articles on mathematical methods for undergraduates. In connection with the article on simplex optimization ( I ) , it should be pointed out that there exists agreatly simplified version of the variable-size simplex algorithm that is very reliable and short enough for programmable pocket calculators such as the HP-67. Replace the reflection ( R ) operation with a diminished expansion (DE)operation: DE = p + F(p - W), where F is a number not much larger than unity (such as 1.25). If DE is better than N , retain DE so that the new simplex is (B, DE,N). If DE is worse than N , take the new simplex as (B, N, Cw). These two operations require only nine storage registers (2). That response surfaces are invariably Euclidean is so thoroughly ingrained in our minds that to think otherwise seems peculiar. Yet it is possible to execute simplex optimization in other types of space (3). The problem of least-squares treatments when both X and Y contain errors certainlv belongs in the undereraduate curriculum (4). hut the eas:est way to introduce ;he subject is nrobablv hv means of the least-distances line. The reader can find a p i e i a n t discourse on this subject in Prahl's recent article (5). Prahl's algorithm is easily incorporated into the programmable pocket calculator. Literature Cited (1) Isgastt,D.J., J. CHUM.EDUC.,60707 (1983).
To the Editor:
G. L. Silver Monsanto Research Corporation-Mound Miamisburg. OH 45342
The method of least distances proposed by Prahl is based on the assumption that the rrrori in x and y are equal and constant from point to point. Prahl's treatment is therefore not genernlly applicable to all data as an exact solution, hut in fairness to the approach, does give an exact solution for the s l o ~ and e interce~tof the line of bevt fit when this condition is met. In addition. the treatment hv Prahl does not ~rovideakarithms for calculating the errors in the slope and intercept 01' the line of best fit. which are imwrtant bemuse many.. phvsical . constants are obtained from these quantities and it is desirable to accompany these physical constants with appropriate error estimates. It is possible that Prahl's treatment could be extended to provide this information. T. I. Ouickenden Universiiy of Western Aunralia Nedlands, Western Australia 6009
Volume 61 Number 8 August 1984
743
