  The restriction imposed on the J-matrix method of using specific L2 bases is
lifted without compromising any of the advantages that it offers. This opens
the door to a wider range of application of the method to physical problems
beyond the restrictive SO(2,1) dynamical symmetry. The numerical scheme
developed to achieve this objective projects the J-matrix formalism in terms of
the eigenvalues of a finite Hamiltonian matrix and its submatrices in any
convenient L2 basis. Numerical stability and convergence of the original
analytic J-matrix method is still maintained in the proposed scheme, which can
be applied to multi-channel nonrelativistic as well as relativistic scattering
problems.
