Hurwitz polynomials and orthogonal polynomials generated by Routh-Markov parameters

DOI10.1007/s00009-018-1083-2zbMath1390.26026OpenAlexW2791509707MaRDI QIDQ1635733

Abdon Eddy Choque Rivero

Publication date: 1 June 2018

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-018-1083-2

zbMATH Keywords

orthogonal polynomialscontinued fractionsMarkov parametersHurwitz polynomialsRouth algorithm

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Stability of solutions to ordinary differential equations (34D20) Real polynomials: location of zeros (26C10)

Related Items (4)

On resolvent matrix, Dyukarev-Stieltjes parameters and orthogonal matrix polynomials via \([0, \infty)\)-Stieltjes transformed sequences ⋮ Resolvent matrix of the truncated Nevanlinna-Pick matrix interpolation problem via orthogonal rational functions in the Stieltjes class ⋮ A Favard type theorem for Hurwitz polynomials ⋮ The matrix Toda equations for coefficients of a matrix three-term recurrence relation

Cites Work

• From the Potapov to the Krein-Nudel'man representation of the resolvent matrix of the truncated Hausdorff matrix moment problem
• Elementary proof of the Routh-Hurwitz test
• An elementary proof of the Routh-Hurwitz stability criterion
• A sufficient condition for a polynomial to be stable
• Application of Hankel matrices of Markov parameters to the solutions of the Routh-Hurwitz and the Schur-Cohn problems
• Relations between the orthogonal matrix polynomials on \([a,b\), Dyukarev-Stieltjes parameters, and Schur complements]
• Euclid algorithm, orthogonal polynomials, and generalized Routh-Hurwitz algorithm
• On Dyukarev's resolvent matrix for a truncated Stieltjes matrix moment problem under the view of orthogonal matrix polynomials
• On matrix Hurwitz type polynomials and their interrelations to Stieltjes positive definite sequences and orthogonal matrix polynomials
• Structured Matrices, Continued Fractions, and Root Localization of Polynomials
• An elementary proof of Kharitonov's stability theorem with extensions
• The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations
• On Kharitonov-type results for complex-coefficient interval Schur polynomials
• Sign patterns of the Schwarz matrices and generalized Hurwitz polynomials
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