Algorithms for Quadratic Matrix and Vector Equations by Federico PoloniAlgorithms for Quadratic Matrix and Vector Equations by Federico Poloni

Algorithms for Quadratic Matrix and Vector Equations

byFederico Poloni

Paperback | November 11, 2011

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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.

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Title:Algorithms for Quadratic Matrix and Vector EquationsFormat:PaperbackDimensions:250 pages, 9.45 × 6.61 × 0.04 inPublished:November 11, 2011Publisher:Scuola Normale SuperioreLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:8876423834

ISBN - 13:9788876423833

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Table 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.