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Algorithms for Quadratic Matrix and Vector Equations (Publications of the Scuola Normale Superiore 16)

Algorithms for Quadratic Matrix and Vector Equations (Publications of the Scuola Normale Superiore 16)

By: Federico Poloni (author)Paperback

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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.


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.

Product Details

  • ISBN13: 9788876423833
  • Format: Paperback
  • Number Of Pages: 250
  • ID: 9788876423833
  • ISBN10: 8876423834

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