Algorithms for Quadratic Matrix and Vector Equations

This book is devoted to studying algorithms for the solution of a class of quadratic matrix and vector equations. These equations appear, in different forms, in several practical applications, especially in applied probability and control theory. The equations are first presented using a novel unifying approach; then, specific numerical methods are presented for the cases most relevant for applications, and new algorithms and theoretical results developed by the author are presented. The book focuses on "matrix multiplication-rich" iterations such as cyclic reduction and the structured doubling algorithm (SDA) and contains a variety of new research results which, as of today, are only available in articles or preprints.

List of contents

Linear algebra preliminaries.- Quadratic vector equations.- A Perron vector iteration for QVEs.- Unilateral quadratic matrix equations.- Nonsymmetric algebraic Riccati equations.- Transforming NAREs into UQMEs.- Storage optimal algorithms for Cauchy-like matrices.- Newton method for rank-structured algebraic Riccati equations.- Lur'e equations.- Generalized SDA.- An effective matrix geometric mean.- Constructing other matrix geometric means.

Product details

• Authors: Federico Poloni
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 11.11.2011
• EAN: 9788876423833
• ISBN: 978-88-7642-383-3
• No. of pages: 250
• Illustrations: 250 p.
• Series: Publications of the Scuola Normale Superiore; Theses (Scuola Normale Superiore)
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra