Spline interpolation and optimal error determination

The smoothing of the spectroscopic curves and their derivatives is examined in this study. These operations which have been done on the experimntal data are a curve fitting operation. The number of optimal curves which will provide the best smoothing in the spektroscopic curves is determined. In the firs stage, the divided differences and polinomal interpolation are explained. In the second stage, the B-Spline functions used in the function of piecewise interpolation and their features are explained. In the third stage, in order to obtain the B-Spline functions, the recurrence relation is ffound out. In the fourth stage, so as to find the interpolation functions to the seventh degree and knot point are explained. In the sixth stage, for UV spectrum data of the mixture of Fe(III)-Bi(III) and Gauss curve the number of errors in different B-Spline degress are showed in the graphics. The occilation is seen in the interpolation function obtained by using 150 knot points Thr mos regular curve is obtained in the number of point which is the error in minumum degree. Although the error is small oscillation occurs in the curve as the number of point increases. Taking in derivatives of the spectral curves is solved vy using the high degrees of the spline functions. Whwn the optimal knot is used, the oscilation is not seen in derivative curves.