Linear interpolation problems for matrix classes and a transformational characterization of M-matrices

Abstract The linear interpolation problem (LIP) for a class of matrices C asks for which pairs of vectors x, y there exists a matrix A∈ C such that Ax=y . The LIP is solved for M-matrices, P-matrices, H-matrices, and H + -matrices. In addition, a transformational characterization is given for M-matrices that refines the known one for P-matrices. There is no such characterization for H- or H + -matrices.