Least Squares Fitting of Exponential Functions

摘要

In attempting to fit an exponential function to a set of data points by the method of least squares, the general situation is that the equations resulting from partial differentiation are transcendental in one or more of the parameters and cannot be solved by the usual algebraic methods. This paper develops two methods for dealing with the above difficulty. The first method employs Newton's Formula to fit the general form f(x) = alpha + beta(x to the power a)(e to the power(gamma(x to the power b))). The second method employs numerical analytic methods to fit the form f(x) = alpha + beta(e to the power(gamma x)). (Author)