Piecewise least squares fitting technique using finite interval method with Hermite polynomials

Experimental fire research often produces large amounts of data. Effective methods of preprocessing the data are needed to filter out irrelevant scatter and to make the data analysis easier. Curve fitting techniques are often needed to smooth out scattered experimental data to permit the application of analytical formulae which often involve derivatives of the data function. One of the critical features in fitting the data is to avoid discontinuous changes in curvature and slope, in cases where the associated oscillations in derivatives are physically meaningless. A working piecewise fitting technique based on the approximation technique of the finite element method is presented in association with the calculation of the confidence interval for the fitted function and its first and second derivatives. The approximation assumes the fitted function and its derivatives up to the second order to be continuous. The ideas presented below are then materialized into the creation of a performing software package programmed in standard FORTRAN 77. Given a sufficient set of data points (pairs) this software performs the fitting and calculates the confidence intervals of the fitted function, and its first and second derivatives.