Data Fitting

  • Sun-Chong Wang
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 743)


An experimenter, to test the ideas or theories in mind, prepares her experiment. She excites the sample by a well controlled means. Reactions from the sample are measured by appropriate apparatus. The next step is to compare the recorded data with the theory. The task of comparison is most usually practiced by the method of chi-square (or least squares) fitting. Another application of chi-square fits is in data interpolation/extrapolation. Since chi-square fits are so commonly used by researchers in data analysis, we demonstrate a class which performs a 2-dimensional chi-square fit.


Monte Carlo Technique Marquardt Method Monte Carlo Data Trial Parameter Arbitrary Distribution Function 
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  1. The Levenberg-Marquardt method was suggested by Levenberg and put forth by Marquardt in, D.W. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters”, J. Soc. Ind. Appl. Math., 11, (1963) 431–441MathSciNetzbMATHCrossRefGoogle Scholar
  2. A textbook on statistical data analysis is, PR. Bevington, “Data Reduction and Error Analysis for the Physical Sciences”, McGraw-Hill Book Co., New York (1969)Google Scholar
  3. A similar Marquardt method in C can be found in section 14.4 of, W.H. Press, B.P Flannery, S.A. Teukolsky, and W.T. Vetterling, “Numerical Recipes in C”, Cambridge University Press, New York (1988)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Sun-Chong Wang
    • 1
  1. 1.TRIUMFCanada

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