Comparison of curve fitting techniques

Abstract

SUMMARYVarious methods of curve fitting used in solving aero-thermodynamic problems of turbomachines have been compared. The first and second derivatives predicted by using orthogonal polynomial fits are much more accurate than those obtained by using spline fits (with different boundary conditions) and method of least squares.

Discussion: “Fluid Dynamic Excitation of Centrifugal Compressor Rotor Vibrations” (Thompson, W. E., 1978, ASME J. Fluids Eng., 100, pp. 73–78)

“…Spline fit with two types of end conditions was found to be inferior to least square and orthogonal polynomial fits [33]. Since spline curve provides a very simple analytical method for curve fits an effort was made to obtain a very accurate spline by choosing the best possible end conditions and using various schemes like spline on spline and smoothing etc.…”