  We present a new algebraic method for solving the inverse problem of quantum
scattering theory based on the Marchenko theory. We applied a triangular wave
set for the Marchenko equation kernel expansion in a separable form. The
separable form allows a reduction of the Marchenko equation to a system of
linear equations. For the zero orbital angular momentum, a linear expression of
the kernel expansion coefficients is obtained in terms of the Fourier series
coefficients of a function depending on the momentum $q$ and determined by the
scattering data in the finite range of $q$. It is shown that a Fourier series
on a finite momentum range ($0<q<\pi/h$) of a $q(1-S)$ function ($S$ is the
scattering matrix) defines the potential function of the corresponding radial
Schr\"odinger equation with $h$-step accuracy. A numerical algorithm is
developed for the reconstruction of the optical potential from scattering data.
The developed procedure is applied to analyze the $^{1}S_{0}NN$ data up to 3
GeV. It is shown that these data are described by optical energy-independent
partial potential.
