The condition number of the double-period method

Abstract

The double period method [1] uses special trigonometric series for approximation and extrapolation of nonperiodical functions. It has a number of advantages in comparison with other methods. In the previous work [2], the properties of the method and its parameters were studied from the standpoint of solving applied problems. However, the precision of the method was estimated empirically, on the basis of studying the model examples. The principal difficulty is the need to solve an ill posed system of linear equations. This work is devoted to studying the condition number of the matrix of the double period method. The optimal parameters of the method are adjusted to allow con trolling the arithmetic calculation errors and achieving better approximation accuracy.