Interpolation, Differentiation, Data Smoothing, and Least Squares Fit to Data With Decreased Computational Overhead

In many experimental and industrial situations, data is sampled at predefined but irregular intervals by a small dedicated microcomputer. This paper details a general method of fitting such data to an Nth-order polynomial according to the least square criterion. The approach can be used to decrease the extensive computational overhead needed to evaluate the simultaneous equations used in other least square fit algorithms making it suitable for use with small systems. Methods of differentiation, interpolation, and data smoothing are detailed. Estimates of the errors in the fitting parameters are given. This method provides an insight into limitations of the least square fit method normally obscured in other algorithms. The computational time saving increases as the polynomial order N increases. Two applications are briefly discussed.