M. Shmoish, ON GENERALIZED SPECTRAL FUNCTIONS, THE PARAMETRIZATION OF BLOCK HANKEL AND BLOCK JACOBI MATRICES, AND SOME ROOT LOCATION-PROBLEMS, Linear algebra and its applications, 202, 1994, pp. 91-128
The parametrization of a strongly regular block Hankel matrix in terms
of certain block entries of an appropriately chosen sequence of block
inverses is established. This leads to a new recipe for solving the g
eneralized spectral problem for jacobi matrices. A generalized spectra
l function is introduced and, together with the parametrization referr
ed to above, is used to investigate the root location of certain ortho
gonal matrix polynomials. The matrix analogues of two classical stabil
ity tests are discussed.