The Singular Method of Exponential Approximation With its Applications

Abstract

The singular spectral variant of exponential approximation is developed, which combines the order reduction of a polynomial by the singular method of the matrix beams on the first stage and recovering of the exponential polynomial of reduced order by the method of z-approximation on the second stage. Examples of this method application are presented typical for the circuit theory and radio electronics. In particular, the approximation of Bessel functions with accuracy ∝ 10–12 ••• 10–11is performed on the interval (0, 100π) by exponential polynomial of 28th order; the nine-stage amplifier order by sequential application of the methods of abbreviated operator equations and matrix beams is reduced three times with the absolute error of AFC approximation less than 3.10−3; the identification problem of sequence parameters for radar pulses is solved at signal/noise ratio in the range from 30 to 0 dB. Other possible areas of this method application are considered.