The influence of the smoothness of interpolating trigonometric splines on interpolation error

Denysiuk, Volodymyr; Negodenko, Elena
October 2013
Ukrainian Food Journal;2013, Vol. 2 Issue 4, p570
Academic Journal
Introduction. The theory of algebraic interpolated polynomials has some drawbacks: the older members of polynomials rapidly increase with the degree of polynomials used; they rarely leads to any reasonable physical interpretation of the obtained approximations. When modeling it is acute to apply polynomial spline functions or simple splines. Materials and methods. To identify the impact of smoothness of interpolated trigonometric splines to the interpolation error there are applied theoretical study and mathematical modeling in software package MathCAD. Results. The influence of differential properties of trigonometric interpolated splines to the interpolation error was determined. There was also defined the impact of spline smoothness properties to the interpolation error at both ends and in the middle of a segment in test cases; there was found that with the increase of spline order the interpolation error increases. It is explained by the fact that with the increase of spline order the harmful effects of the Gibbs phenomenon reinforce.


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