Solving Symmetric Algebraic Riccati Equations with High Order Iterative Schemes

  1. Hernández-Verón, M.A. 1
  2. Romero, N. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Mediterranean Journal of Mathematics

ISSN: 1660-5446

Año de publicación: 2018

Volumen: 15

Número: 2

Tipo: Artículo

DOI: 10.1007/S00009-018-1092-1 SCOPUS: 2-s2.0-85043231215 GOOGLE SCHOLAR

Otras publicaciones en: Mediterranean Journal of Mathematics

Proyectos relacionados

Ecuaciones no lineales y métodos iterativos. Aplicaciones a problemas de optimización y ecuaciones matriciales. Nonlinear equations and iterative methods. Applications to optimization problems and matrix equations.

2015/00069/001

Resumen

We solve symmetric algebraic Riccati equation using efficient high-order iterative schemes which improve the speed of convergence of others widely used in the literature. These high-order iterative schemes involve the Riccati operator and the first Fréchet derivative. Applying these iterative schemes is equivalent to solving a fixed number of Lyapunov equations with the same matrix. This key fact makes efficient these methods. Moreover, a local convergence result of one of these high-order iterative schemes is analyzed. Finally, numerical experiments confirm the advantageous performance of these schemes. © 2018, Springer International Publishing AG, part of Springer Nature.