Document Open Access Logo

From Algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms

Authors Dario A. Bini, Beatrice Meini, Federico Poloni

Thumbnail PDF


  • Filesize: 339 kB
  • 28 pages

Document Identifiers

Author Details

Dario A. Bini
Beatrice Meini
Federico Poloni

Cite AsGet BibTex

Dario A. Bini, Beatrice Meini, and Federico Poloni. From Algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-28, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2008)


The problem of reducing an algebraic Riccati equation $XCX-AX-XD+B=0$ to a unilateral quadratic matrix equation (UQME) of the kind $PX^2+QX+R$ is analyzed. New reductions are introduced which enable one to prove some theoretical and computational properties. In particular we show that the structure preserving doubling algorithm of B.D.O. Anderson [Internat. J. Control, 1978] is nothing else but the cyclic reduction algorithm applied to a suitable UQME. A new algorithm obtained by complementing our reductions with the shrink-and-shift tech- nique of Ramaswami is presented. Finally, faster algorithms which require some non-singularity conditions, are designed. The non-singularity re- striction is relaxed by introducing a suitable similarity transformation of the Hamiltonian.
  • Algebraic Riccati Equation
  • Matrix Equation
  • Cyclic Reduction
  • Structured doubling algorithm


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail