Second method of Liapunov and Routh's canonical form

Sign patterns of the Schwarz matrices and generalized Hurwitz polynomials

“…[14,4]). Note that Wall's work [17] where he considered Hurwitz stable polynomials as characteristic polynomials of matrices (2.9) with positive b k appeared earlier than the paper [15] by H. Schwarz.…”

“…[2,14,3,4,5,6] and references there). Here we use the method due to Wall [17,18] to solve the inverse spectral problem and our results on the generalized Hurwitz polynomials to solve the direct spectral problem for the Schwarz matrices (1.1) with a wide class of sign patterns.…”

On the spectra of Schwarz matrices with certain sign patterns

“…These matrices are well-studied from the matrix theory point of view (see e.g. [2,14,3,4,5,6] and references there). Here we use the method due to Wall [17,18] to solve the inverse spectral problem and our results on the generalized Hurwitz polynomials to solve the direct spectral problem for the Schwarz matrices (1.1) with a wide class of sign patterns.…”

“…Thus this theorem solves the direct and inverse spectral problems for stable Schwarz matrices, that is, the Schwarz matrices with positive b k , that are sometimes called Routh canonical forms (see e.g. [14,4]). Note that Wall's work [17] where he considered Hurwitz stable polynomials as characteristic polynomials of matrices (2.9) with positive b k appeared earlier than the paper [15] by H. Schwarz.…”