Аннотация:In a number of physical problems, one needs to approximate experimental curves measured with large errors. An important example is processing of thermonuclear reaction cross sections and calculating of reaction rates basing on them. In the present paper, we have constructed regularized double period method. This method not only provides good approximation but also allows to extrapolate the latter beyond the boundaries of experimental measurements. We have developed a method of estimating the confidence interval of the obtained curve. The proposed methods are used to approximate the cross sections of 4 reactions which are the most important for the problem of controlled thermonuclear fusion. The obtained accuracy is ≤ 0.3%. Using these cross sections, the thermonuclear reaction rates are calculated. Their error is ≤ 4 % which is ∼ 5 times more accurate than the known approximations.