Least square fitting with one explicit parameter less

Abstract

It is shown that whenever the multiplicative normalization of a fitting function is not known, least square fitting by χ2 minimization can be performed with one parameter less than usual by converting the normalization parameter into a function of the remaining parameters and the data. Program summaryProgram title: FITM1Catalogue identifier: AEYG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYG_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 354261No. of bytes in distributed program, including test data, etc.: 2627533Distribution format: tar.gzProgramming language: Fortran 77 with standard extensions (tested with g95 on a Mac).Computer: Any which supports a Fortran 77 compatible compiler.Operating system: Any with a Fortran 77 compatible compiler.RAM: 1 MbyteClassification: 4.9.Nature of problem: Least square minimization when one of the free parameters is the multiplicative normalization of the fitting function.Solution method: Conversion of the normalization constant into a function of the other parameters and the data, resulting into one explicit fitting parameter less.Running time: Less than 1 s on modern PCs