Algorithms for Quadratic Matrix and Vector Equations

2011
ISBN: 978-88-7642-383-3
Verlag: Scuola Normale Superiore

Buch, Englisch, 250 Seiten, Format (B × H): 154 mm x 243 mm, Gewicht: 446 g

Reihe: Theses (Scuola Normale Superiore)

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.

Poloni, Federico

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.