The Schur algorithm is a signal processing algorithm which works on a layer‐stripping principle. Its time‐domain version, the fast Cholesky recursion, is a fast and efficient algorithm well‐suited for high‐speed data processing. In this paper, these algorithms are applied to the inverse problem for a continuous layered acoustic medium. Three different excitations of the medium are considered: impulsive plane waves at normal incidence, impulsive plane waves at oblique incidence, and spherical waves emanating from an impulsive point source. The fast algorithms obtained for each of these problems seem to be computationally superior to past work done on these problems that employed Gelfand–Levitan theory to reconstruct the potential of a Schrödinger equation.