  We propose a high precision algorithm for solving the
Gelfand-Levitan-Marchenko equation. The algorithm is based on the block version
of the Toeplitz Inner-Bordering algorithm of Levinson's type. To approximate
integrals, we use the high-precision one-sided and two-sided Gregory quadrature
formulas. Also we use the Woodbury formula to construct a computational
algorithm. This makes it possible to use the almost Toeplitz structure of the
matrices for the fast calculations.
