  An inverse spectral problem is studied for the matrix Sturm-Liouville
operator on a finite interval with the general self-adjoint boundary condition.
We obtain a constructive solution based on the method of spectral mappings for
the considered inverse problem. The nonlinear inverse problem is reduced to a
linear equation in a special Banach space of infinite matrix sequences. In
addition, we apply our results to the Sturm-Liouville operator on a star-shaped
graph.
