Algorithms for Quadratic Matrix and Vector Equations

ISBN-13: 9788876423833 / Angielski / Miękka / 2011 / 250 str.

Federico Poloni

Opis

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."

Spis treści

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.