IMPROVING THE EFFICIENCY OF EXPERIMENTAL DATA PROCESSING AT CUBIC SPLINES’ INTERPOLATION BY “THE SHIFT TECHNIQUE”

Abstract

Introduction. To process the experimental data, interpolation and smoothing cubic splines are widely used in practice. This task is relevant and attracts a sufficiently large number of researchers. To make contribution to the solution of this difficult problem, the author previously proposed “the shift technique”. The author sets the task of comparing such methodology with the well-known and widely used method of spline-smoothing.

Methods and materials. In this article two methods of processing experimental data at interpolation by cubic splines are compared. The first technique is based on the use of smoothing cubic splines (smoothing splines) in the processing of experimental data. The second one is based on the use of “the shift technique” based on the shift points of stitching together fragments of cubic parabolas, which are relative to the interpolation nodes linked to the experimental data. To compare the effectiveness of both methods, the Gaussian distribution (normal distribution) is chosen as the test curve.

Results and discussion. The calculated data obtained by the two above-mentioned methods are presented in tabular and graphical forms for greater visibility. It follows that the obtained calculations with “the shift technique “ at the nodes in which the greatest deviations of the calculated data from the theoretical values of the normal distribution, are observed in the article. Therefore, the possibility to reduce the error introduced into the normal distribution by an average of at least twice is discussed.

Conclusion. As a result of a comparative analysis of the calculated data obtained using the two methods, the author concludes that “the shift technique” in the test-performed program show better results that are in good agreement with the normal distribution within the error made to the test curve.