  The method of constructing Hermite trigonometric polynomials, which
interpolate the values of a certain periodic function and its derivatives up to
(including ) the -th ( ) order in nodes of a uniform grid, is considered. The
proposed method is based on the properties of the periodicity of trigonometric
functions and is reduced to the solving of only two systems of the linear
algebraic equations of the --th order; solutions to these systems may be
obtained in advance. When implementing this method, it is necessary to
calculate the coefficients of interpolation trigonometric polynomials that
interpolate the values of the function itself and the values of its derivatives
in the nodes of a uniform grid; well-known algorithms of fast Fourier transform
can be applied for this purpose. The examples of construction of Hermite
trigonometric polynomials for .. are given. The proposed method may be
recommended for wide practical application.
