Application of Universal Fast Trigonometric Interpolation and Extrapolation for Determining the Launch Point Coordinates of a Flight Vehicle

The foundations of fast universal trigonometric interpolation for nonperiodic functions used to obtain high-accuracy approximate solutions are described. High-accuracy formulas are derived for computing the launch point coordinates of a flight vehicle by applying universal fast trigonometric interpolation combined with extrapolation at the endpoints of a given interval. Numerical experiments show that, after launching the first vehicle, the launch point coordinates can be determined in 7 s with accuracy of \({{10}^{{ - 17}}}\) m.