Regularization of the double period method for experimental data processing

A. A. Belov ; N. N. Kalitkin

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 11, pp. 1771-1781

Résumé

In physical and technical applications, an important task is to process experimental curves measured with large errors. Such problems are solved by applying regularization methods, in which success depends on the mathematician’s intuition. We propose an approximation based on the double period method developed for smooth nonperiodic functions. Tikhonov’s stabilizer with a squared second derivative is used for regularization. As a result, the spurious oscillations are suppressed and the shape of an experimental curve is accurately represented. This approach offers a universal strategy for solving a broad class of problems. The method is illustrated by approximating cross sections of nuclear reactions important for controlled thermonuclear fusion. Tables recommended as reference data are obtained. These results are used to calculate the reaction rates, which are approximated in a way convenient for gasdynamic codes. These approximations are superior to previously known formulas in the covered temperature range and accuracy.