A simple piecewise cubic spline method for approximation of highly nonlinear data

Abstract

Approximation methods are used in the analysis and prediction of data, especially laboratory data, in engineering projects. These methods are usually linear and are obtained by least-square-error approaches. There are many problems in which linear models cannot be applied. Because of that there are logarithmic, exponential and polynomial curve-fitting models. These nonlinear models have a limited application in engineering problems. The variation of most data is such that the nonlinearity cannot be approximated by the above approaches. These methods are also not applicable when there is a large amount of data. For these reasons, a method of piecewise cubic spline approximation has been developed. The model presented here is capable of following the local nonuniformity of data in order to obtain a good fit of a curve to the data. There is C 1 continuity at the limits of the piecewise elements. The model is tested and examined with four problems here. The results show that the model can approximate highly nonlinear data efficiently.