The condition number of the double-period method

The double-period method [1] uses special trigonometric series decomposition for approximation and extrapolation of smooth non-periodical functions. It has a number of advantages. In paper [2] the method and its properties and parameters were studied for concrete applications. However the method accuracy was estimated empirically, basing on the model cases considered. The principal difficulty is the need to solve an ill-posed system of linear equations. Proposing a new adequate condition criteria and applying it to the method is the main subject of this study. Optimal parameters of the method proposed in [2] are adjusted to allow controlling arithmetic calculation error and achieve better accuracy of the approximation.