Federico Poloni

Algorithms for Quadratic Matrix and Vector Equations (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Scuola Normale Superiore
• Seitenzahl: 250
• Erscheinungstermin: 13. März 2012
• Englisch
• ISBN-13: 9788876423840
• Artikelnr.: 37412949

Inhaltsangabe

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.