  In this work the numerical solution of acoustic tomography problem based on
the iterative and functional-analytical algorithms is considered. The
mathematical properties of these algorithms were previously described in works
of R.G.Novikov for the case of the Schr\"odinger equation. In the present work,
for the case of two-dimensional scalar Helmholtz equation, the efficiency of
the iterative algorithm in reconstruction of middle strength scatterers and
advantages of the functional-analytical approach in recovering strong
scatterers are demonstrated. A filtering procedure is considered in the space
of wave vectors, which additionally increases the convergence of the iterative
algorithm. Reconstruction results of sound speed perturbations demonstrate the
comparable noise immunity and resolution of the considered algorithms when
reconstructing middle strength scatterers. A comparative numerical
investigation of the iterative and functional-analytical algorithms in inverse
acoustic scattering problems is implemented in this work for the first time.
