Poloni Algorithms for Quadratic Matrix and Vector Equations
1. Auflage 2012
ISBN: 978-88-7642-384-0
Verlag: Edizioni della Normale
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 250 Seiten, eBook
Reihe: Theses (Scuola Normale Superiore)
ISBN: 978-88-7642-384-0
Verlag: Edizioni della Normale
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
