Given a polynomial of degree n, a test of script O sign (n2) elementary operations and growth factor 1 is presented in order to check the Routh-Hurwitz conditions. This optimal growth factor guarantees that the test presents better stability properties than other known tests. We also present a test of script O sign (n3) elementary operations and growth factor 1 in order to check if a matrix is strictly totally positive. Finally, totally positive matrices are characterized by their symmetric-triangular decompositions. ?? 2003 Elsevier Inc. All rights reserved.
Pe??a, J. M. (2004). Characterizations and stable tests for the Routh-Hurwitz conditions and for total positivity. Linear Algebra and Its Applications, 393(1–3), 319–332.