An Online Display for the Study of Approximating Functions

ABSTRACT

The method of least squares is often used to determine the arbitrary constants in an empirical formula or approximating function. If such a function is not linear in its unknowns, approximate values must first be obtained. Typically they are obtained graphically or as the result of physical supposition or similar experiment. This paper describes a program written to find first approximations for certain oscilloscope traces by: (1) displaying the trace on a cathode-ray tube (CRT) and, (2) imposing upon it a computer generated curve which (3) employs parameters arbitrarily supplied by an operator in a quest for visual coincidence. While the technique proved successful in this application, a greater value may lie in its having indicated a mechanism for further automation. In its present form the method might best be utilized as a tool for studying the behavior of selected approximating functions.

REFERENCES

• 1: HULSE, E. H. Electronic instrumentation for mlclear device explosions. UCRL-7251, Lawrence Radiation Lab, U. of CMifornia, Livermore, 1963.
• 2: ADAMS, W. M., AND ALLEN, D. C. Reading seismograms with digitM computers. Bull. Seismological Soc. of Amer. 51, 1 (1961).
• 3: McMAsTEts, W.H. Measurement of Gaussian signMs by Rossi anMysis. Mere., Lawrence Radiation Lab, U. of Calif., Livermore.
• 4: SCaBOROUGH, J. B. Numerical Mathematical Analysis. 3rd ed., Johns HopkiiLs U. Press, Baltimore, 1955.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Measurement, Performance, Theory