Open AccessA simple piecewise cubic spline method for approximation of highly nonlinear data
Author(s) -
Mehdi Zamani
Publication year - 2012
Publication title -
natural science
Language(s) - English
Resource type - Journals
eISSN - 2150-4105
pISSN - 2150-4091
DOI - 10.4236/ns.2012.41012
Subject(s) - piecewise , spline (mechanical) , nonlinear system , curve fitting , mathematics , piecewise linear function , logarithm , polynomial , exponential function , mathematical optimization , approximation error , simple (philosophy) , mathematical analysis , statistics , philosophy , physics , structural engineering , epistemology , quantum mechanics , engineering
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 C1 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