Computing χ2 values

  • Authors:

  • John F. Dooley;Daniel C. St. Clair;William E. Bond

  • Affiliations:

  • Motorola Urbana Design Center 1101 East University Avenue Urbana, IL and Department of McDonnel Douglas Research Loaboratories, St. Louis, MO;University of Missouri-Rolls Engineering Education Center, St. Louis, MO;McDonnell Douglas, Research Laboratories, St. Louis, MO

  • Venue:
  • SIGCSE '94 Proceedings of the twenty-fifth SIGCSE symposium on Computer science education
  • Year:
  • 1994

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Abstract

Textbooks and courses on numerical algorithms contain numerous examples which lead students to believe that the algorithm of choice for computing the zeros of a function f(x) is Newton's algorithm. In many of these courses little or no time is spent in providing students with “real world” experiences where Newton's method fails.The work presented in this paper describes a slow convergence problem encountered while trying to use Newton to estimate values for the &khgr;2 distribution. The problem occurred while the authors were trying to implement a well-known machine learning algorithm from the field of artificial intelligence. The function being evaluated and the convergence problem with Newton's method is described. Numerical results are given that indicate that a hybrid algorithm consisting of Newton and the nonderivative bisection algorithm not only provides good results but quickly and consistently converges.