Algorithms for Quadratic Matrix and Vector Equations
(Sprache: Englisch)
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...
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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.
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.
Inhaltsverzeichnis zu „Algorithms for Quadratic Matrix and Vector Equations “
- 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
Bibliographische Angaben
- Autor: Federico Poloni
- 2012, 239 Seiten, Maße: 15 x 24,1 cm, Kartoniert (TB), Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 8876423834
- ISBN-13: 9788876423833
Sprache:
Englisch
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