  We propose a new method for solving the Gelfand-Levitan-Marchenko equation
(GLME) based on the block version of the Toeplitz Inner-Bordering (TIB) with an
arbitrary point to start the calculation. This makes it possible to find
solutions of the GLME at an arbitrary point with a cutoff of the matrix
coefficient, which allows to avoid the occurrence of numerical instability and
to perform calculations for soliton solutions spaced apart in the time domain.
Using an example of two solitons, we demonstrate our method and its range of
applicability. An example of eight solitons shows how the method can be applied
to a more complex signal configuration.
