Algorithms for Quadratic Matrix and Vector Equations

  • Federico Poloni

Part of the Tesi/Theses book series (PSNS, volume 16)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Linear algebra preliminaries

    1. Federico Poloni
      Pages 1-11
  3. Quadratic vector and matrix equations

    1. Front Matter
      Pages 13-13
    2. Federico Poloni
      Pages 15-29
    3. Federico Poloni
      Pages 31-45
    4. Federico Poloni
      Pages 47-54
    5. Federico Poloni
      Pages 55-78
    6. Federico Poloni
      Pages 79-99
  4. Rank-structured NAREs

    1. Front Matter
      Pages 101-101
  5. Matrix equations from control theory

    1. Front Matter
      Pages 145-145
    2. Federico Poloni
      Pages 147-158
    3. Federico Poloni
      Pages 159-171
  6. Matrix geometric means

    1. Front Matter
      Pages 173-173
    2. Federico Poloni
      Pages 175-192
    3. Federico Poloni
      Pages 193-209
    4. Federico Poloni
      Pages 211-211
  7. Back Matter
    Pages 213-239

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.


applied probability control theory numerical linear algebra

Authors and affiliations

  • Federico Poloni
    • 1
  1. 1.Sekretariat MA 4–5BerlinGermany

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