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Algorithms for Quadratic Matrix and Vector Equations

  • Book
  • © 2011

Overview

Authors:
  1. Federico Poloni

    1. Sekretariat MA 4–5, Berlin, Germany

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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

Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 16)

Part of the book sub series: Theses (Scuola Normale Superiore) (TSNS)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Linear algebra preliminaries

    1. Linear algebra preliminaries

      • Federico Poloni
      Pages 1-11

  3. Quadratic vector and matrix equations

    1. Front Matter

      Pages 13-13
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    2. Quadratic vector equations

      • Federico Poloni
      Pages 15-29

    3. A Perron vector iteration for QVEs

      • Federico Poloni
      Pages 31-45

    4. Unilateral quadratic matrix equations

      • Federico Poloni
      Pages 47-54

    5. Nonsymmetric algebraic Riccati equations

      • Federico Poloni
      Pages 55-78

    6. Transforming NAREs into UQMEs

      • Federico Poloni
      Pages 79-99

  4. Rank-structured NAREs

    1. Front Matter

      Pages 101-101
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    2. Storage-optimal algorithms for Cauchy-like matrices

      • Federico Poloni
      Pages 103-129

    3. Newton method for rank-structured algebraic Riccati equations

      • Federico Poloni
      Pages 131-143

  5. Matrix equations from control theory

    1. Front Matter

      Pages 145-145
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    2. Lur’e equations

      • Federico Poloni
      Pages 147-158

    3. Generalized SDA

      • Federico Poloni
      Pages 159-171

  6. Matrix geometric means

    1. Front Matter

      Pages 173-173
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    2. An effective matrix geometric mean

      • Federico Poloni
      Pages 175-192

    3. Constructing other matrix geometric means

      • Federico Poloni
      Pages 193-209

    4. Conclusions

      • Federico Poloni
      Pages 211-211

  7. Back Matter

    Pages 213-239
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Keywords

About this book

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.

Authors and Affiliations

  • Sekretariat MA 4–5, Berlin, Germany

    Federico Poloni

Bibliographic Information

  • Book Title: Algorithms for Quadratic Matrix and Vector Equations

  • Authors: Federico Poloni

  • Series Title: Publications of the Scuola Normale Superiore

  • DOI: https://doi.org/10.1007/978-88-7642-384-0

  • Publisher: Edizioni della Normale Pisa

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Scuola Normale Superiore Pisa 2011

  • Softcover ISBN: 978-88-7642-383-3Due: 11 November 2011

  • eBook ISBN: 978-88-7642-384-0Published: 13 March 2012

  • Series ISSN: 2239-1460

  • Series E-ISSN: 2532-1668

  • Edition Number: 1

  • Number of Pages: 250

  • Topics: Algebra

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