Algorithms for Quadratic Matrix and Vector Equations
Seiten
2011
Scuola Normale Superiore (Verlag)
978-88-7642-383-3 (ISBN)
Scuola Normale Superiore (Verlag)
978-88-7642-383-3 (ISBN)
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This book is devoted to studying algorithms for the solution of a class of quadratic matrix and vector equations. 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.
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.
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.
| Reihe/Serie | Publications of the Scuola Normale Superiore ; 16 | Theses (Scuola Normale Superiore) |
|---|---|
| Zusatzinfo | 250 p. |
| Verlagsort | Pisa |
| Sprache | englisch |
| Maße | 168 x 240 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Schlagworte | applied probability • Control Theory • numerical linear algebra |
| ISBN-10 | 88-7642-383-4 / 8876423834 |
| ISBN-13 | 978-88-7642-383-3 / 9788876423833 |
| Zustand | Neuware |
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