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© 2019

Low-Rank Approximation

Algorithms, Implementation, Applications

Book

Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ivan Markovsky
    Pages 1-34
  3. Linear Modeling Problems

    1. Front Matter
      Pages 35-35
    2. Ivan Markovsky
      Pages 37-70
    3. Ivan Markovsky
      Pages 71-98
    4. Ivan Markovsky
      Pages 99-134
  4. Applications and Generalizations

    1. Front Matter
      Pages 135-135
    2. Ivan Markovsky
      Pages 137-160
    3. Ivan Markovsky
      Pages 161-172
    4. Ivan Markovsky
      Pages 173-197
    5. Ivan Markovsky
      Pages 199-223
  5. Back Matter
    Pages 225-272

About this book

Introduction

This book is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory with a range of applications from systems and control theory to psychometrics being described. Special knowledge of the application fields is not required.

The second edition of /Low-Rank Approximation/ is a thoroughly edited and extensively rewritten revision. It contains new chapters and sections that introduce the topics of:

• variable projection for structured low-rank approximation;
• missing data estimation;
• data-driven filtering and control;
• stochastic model representation and identification;
• identification of polynomial time-invariant systems; and
• blind identification with deterministic input model.

The book is complemented by a software implementation of the methods presented, which makes the theory directly applicable in practice. In particular, all numerical examples in the book are included in demonstration files and can be reproduced by the reader. This gives hands-on experience with the theory and methods detailed. In addition, exercises and MATLAB^® /Octave examples will assist the reader quickly to assimilate the theory on a chapter-by-chapter basis.

“Each chapter is completed with a new section of exercises to which complete solutions are provided.”

Low-Rank Approximation (second edition) is a broad survey of the Low-Rank Approximation theory and applications of its field which will be of direct interest to researchers in system identification, control and systems theory, numerical linear algebra and optimization. The supplementary problems and solutions render it suitable for use in teaching graduate courses in those subjects as well.

Keywords

Data Approximation Linear Algebra Linear Models Low-complexity Model Numerical Algorithms System Identification System Theory Time-invariant System Matrix Completion Toeplitz Problems Hankel Problems Sylvester Problems

Authors and affiliations

  1. 1.Department ELECVrije Universiteit BrusselBrusselsBelgium

About the authors

Ivan Markovsky obtained Ph.D. in Electrical Engineering from the Katholieke Universiteit Leuven in 2005. Since then, he is teaching and doing research in control and system theory at the School of Electronics and Computer Science (ECS) of the University of Southampton and the Department of Fundamental Electricity and Instrumentation (ELEC) of the Vrije Universiteit Brussel, where he is currently an associate processor. His research interests are structured low-rank approximation, system identification, and data-driven control, topics on which he has published 70 peer-reviewed papers, 7 book chapters, and 2 monographs. He is an associate editor of the International Journal of Control and the SIAM Journal of Matrix Analysis and Applications. In 2011, Ivan Markovsky was awarded an ERC starting grant on the topic of structured low-rank approximation.

Bibliographic information

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Reviews

“Markovsky’s book is certainly well suited for graduate students and more experienced readers, and should also be useful to people who need to apply LRA methods in their daily work.” (Kai Diethelm, Computing Reviews, July 18, 2019)