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 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.
Highlights
There are many cases in engineering activities in which one is confronted with laboratory or field data
Suppose there are n pairs of data values (xi, yi), where these values are obtained from experimental, field or statistical analysis
In the case of the nonuniform variation of data that occurs in most engineering problems, a single cubic spline curve cannot be applied
Summary
There are many cases in engineering activities in which one is confronted with laboratory or field data. Suppose there are n pairs of data values (xi, yi), where these values are obtained from experimental, field or statistical analysis. Sometimes there exist multiple values for yi for each value of xi In such situations, if the curve of f(x) passes between and near to the data points, it is more accurate and smoother than when it passes through all the points exactly. If the curve of f(x) passes between and near to the data points, it is more accurate and smoother than when it passes through all the points exactly In those cases an approximate analysis is more suitable for predicting and assigning the y values. Some more advanced methods in this field are based on B-spline and Bézier curves [5,6,7]. Because of the waviness and the sinusoidal forms of their curves, they are not applicable to engineering problems
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