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<title>AAS 98-206</title><body BGCOLOR="ffffff"> <h2>AAS 98-206</h2> <h2>OPTIMAL BEST FITTING OF NUMERICAL DATA</h2> <h4>D. Mortari - Universita degli Studi "La Sapienza" di Roma, Italy</h4> <h2> Abstract </h2> A new method, which optimizes the best fitting of numerical data, is here presented as applied to an m-degree polynomial. Optimization, which is obtained through a linear variable change representing an expansion/contraction of the abscissas axis, is defined as that which minimizes the condition number of the matrix to be inverted. As a function of the polynomial degree and the number of data, an optimal size of the abscissas data range is computed. Closed-form solutions are provided for first and second order polynomials. The improvement with respect to the existing method is substantial and it is shown by meaningful examples. Optimal Best Fitting is not restricted to a polynomial function but it can be applied to other different fitting functions such as at least: the Legendre orthogonal polynomials, trigonometric and exponential functions. <P><A HREF="http://www.space-flight.org/AAS_meetings/1998_winter/sessions.html">Back</A>