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Numerical Solution of Algebraic Riccati Equations

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Dario A. Bini, Bruno Iannazzo, and Beatrice Meini


2012 / xvi + 250 pages / Softcover / ISBN: 978-1-611972-08-5 / List Price $76.50 / SIAM Member Price $53.55 / Order Code FA09

Keywords; algebraic Riccati equations, numerical methods, nonlinear matrix equations, doubling algorithms, quadratic matrix equations.


This concise and comprehensive treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both practitioners and scholars. It is the first book in which nonsymmetric algebraic Riccati equations are treated in a clear and systematic way. Some proofs of theoretical results have been simplified and a unified notation has been adopted.

Readers will find

  • a unified discussion of doubling algorithms, which are effective in solving algebraic Riccati equations. 
  • a detailed description of all classical and advanced algorithms for solving algebraic Riccati equations and their MATLAB® codes. This will help the reader gain an understanding of the computational issues and provide ready-to-use implementation of the different solution techniques.

This book is intended for researchers who work in the design and analysis of algorithms and for practitioners who are solving problems in applications and need to understand the available algorithms and software. It is also intended for students with no expertise in this area who wish to approach this subject from a theoretical or computational point of view. The book can be used in a semester course on algebraic Riccati equations or as a reference in a course on advanced numerical linear algebra and applications.

About the Authors
Dario A. Bini is Professor of Numerical Analysis at the University of Pisa. A coauthor of two other books on polynomial and matrix computations and on the numerical solution of Markov chains, he specializes in numerical linear algebra and polynomial computations. His Web page is here.

Bruno Iannazzo is a Researcher in Numerical Analysis at the University of Perugia. His main interests are in the field of numerical linear algebra with specific attention to matrix functions and matrix equations. His Web page is www.bezout.dm.unipi.it/iannazzo.

Beatrice Meini is an Associate Professor of Numerical Analysis at the University of Pisa. A coauthor of a book on the numerical solution of structured Markov chains, her research interests are numerical linear algebra and its applications, with a special focus on matrix equations and Markov chains. Her Web page is www.dm.unipi.it/~meini.


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