CXXXIX. The fitting of polynomials to unequally-spaced data

Abstract

Summary A technique is given for carrying out rapidly the computations involved in fitting a polynomial by leastsquares to unequally-spaced data. The technique is obtained by adapting the “triangular resolution” methods of solution of linear equations and inversion of matrices given by Fox (1950) and Fox and Hayes (1951) in a way similar to that in which Guest (1950) has adapted a slower method of Doolittle. The method proposed affords the additional advantage of being able to decide, early in the computation, which degree of polynomial curve is appropriate to the data. The theory is presented to establish the validity of the technique and two numerical examples are carried out to deal with two different sets of requirements. References are made throughout the text to the appropriate sections of the above three papers, but the present paper is intended to be complete in itself, and does not require a prior knowledge of those papers.