FITTING OF POWER SERIES, MEANING POLYNOMIALS, ILLUSTRATED ON BAND-SPECTROSCOPIC DATA.

Abstract

The prototype of fitting polynomials to equally-spaced data - in which the equal-spacing is theoretically precise and the data is accurate to many decimal places - arises in the analysis of band spectra. A hard look at such examples leads to an examination of such diverse issues as: How to formulate such problems, the use of robust/resistant techniques in polynomial regression, which coordinates to use and why, the basic properties of linear least squares, choices in stopping a fit, and improved ways to describe answers. The results and attitudes apply rather directly to other situations where a sum of functions of a single variable are fitted. When two or more different variables, subject to error, blunder, or omission, underlie the carriers to be considered, regression/fitting problems are likely to need not only the considerations presented, but others as well. To a varying extent, the same will be true of nonlinear fitting/regression problems. Two discussions of this paper are presented.