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Birkhäuser - Birkhäuser Mathematics - Scuola Normale Superiore | Algorithms for Quadratic Matrix and Vector Equations

Algorithms for Quadratic Matrix and Vector Equations

Poloni, Federico

2011, 250p.

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  • Contains a new unifying approach to quadratic vector and matrix equations in applied probability
  • Gives new insight on the structured doubling algorithm which can be exploited to develop suitable modifications and generalizations
  • 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.

Content Level » Research

Keywords » applied probability - control theory - numerical linear algebra

Related subjects » Scuola Normale Superiore

Table of contents 

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.

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