  The matrix elements of the multi-channel Jost matrices are written in such a
way that their dependencies on all possible odd powers of channel momenta are
factorized explicitly. As a result the branching of the Riemann energy surface
at all the channel thresholds is represented in them via exact analytic
expressions. The remaining single-valued functions of the energy are expanded
in the Taylor series near an arbitrary point on the real axis. Using the thus
obtained Jost matrices, the $S$-matrix is constructed and then the scattering
cross section is calculated, which therefore depends on the Taylor expansion
coefficients. These coefficients are considered as the adjustable parameters
that are optimized to fit a given set of experimental data. After finding the
coefficients, the resonances are located as zeros of the Jost matrix
determinant at complex energies. Within this approach the $S$-matrix has proper
analytic structure. This enables us not only to locate multi-channel resonances
but also to reproduce their partial widths as well as the scattering cross
section in the channels for which the data are not available.
