| Description |
1 online resource (xvi, 239 pages) |
| Series |
Tesi = Theses ; 16 |
|
CRM series ; v. 16 |
|
Tesi (Pisa, Italy) ; 16.
|
|
CRM series (Pisa, Italy) ; v. 16.
|
| Contents |
Part 1. Linear algebra preliminaries -- Linear algebra preliminaries -- Part I. Quadratic vector and matrix equations -- Quadratic vector equations -- A Perron vector iteration for QVEs -- Unilateral quadratic matrix equations -- Nonsymmetric algebraic Riccati equations -- Transforming NAREs into UQMEs -- Part II. Rank-structured NAREs -- Storage-optimal algorithms for Cauchy-like matrices -- Newton method for rank-structured algebraic Riccati equations -- Part III. Matrix equations from control theory -- Lur'e equations -- Generalized SDA -- Part IV. Matrix geometric means -- An effective matrix geometric mean -- Constructing other matrix geometric means -- Conclusions |
| Summary |
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 |
| Analysis |
Mathematics |
|
Algebra |
|
wiskunde |
|
Mathematics (General) |
|
Wiskunde (algemeen) |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Algorithms.
|
|
Matrices.
|
|
Vector algebra.
|
|
Algorithms
|
|
algorithms.
|
|
MATHEMATICS -- Numerical Analysis.
|
|
Algorithms
|
|
Matrices
|
|
Vector algebra
|
| Genre/Form |
dissertations.
|
|
Academic theses
|
|
Academic theses.
|
|
Thèses et écrits académiques.
|
| Form |
Electronic book
|
| ISBN |
9788876423840 |
|
8876423842 |
|
