Low Rank Approximation

Algorithms, Implementation, Applications

  • Ivan Markovsky

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

Table of contents

  1. Front Matter
    Pages I-X
  2. Linear Modeling Problems

    1. Front Matter
      Pages 33-33
    2. Ivan Markovsky
      Pages 1-32
  3. Linear Modeling Problems

    1. Front Matter
      Pages 33-33
    2. Ivan Markovsky
      Pages 35-72
    3. Ivan Markovsky
      Pages 73-106
  4. Miscellaneous Generalizations

    1. Front Matter
      Pages 133-133
    2. Ivan Markovsky
      Pages 135-177
    3. Ivan Markovsky
      Pages 179-197
    4. Ivan Markovsky
      Pages 199-226
  5. Back Matter
    Pages 227-256

About this book

Introduction

Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications 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. Applications described include:

  • system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification;
  • signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing;
  • machine learning: multidimensional scaling and recommender system;
  • computer vision: algebraic curve fitting and fundamental matrix estimation;
  • bioinformatics for microarray data analysis;
  • chemometrics for multivariate calibration;
  • psychometrics for factor analysis; and
  • computer algebra for approximate common divisor computation.

Special knowledge from the respective application fields is not required. 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® examples will assist the reader quickly to assimilate the theory on a chapter-by-chapter basis.

 

Low Rank Approximation: Algorithms, Implementation, Applications is a broad survey of the 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

Control Control Theory Data Approximation Hankel Linear Algebra Linear Models Low-complexity Model Numerical Algorithms OJ0061 Sylvester System Identification System Theory Time-invariant System Toeplitz

Authors and affiliations

  • Ivan Markovsky
    • 1
  1. 1.School of Electronics & Computer ScienceUniversity of SouthamptonSouthamptonUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-2227-2
  • Copyright Information Springer-Verlag London Limited 2012
  • Publisher Name Springer, London
  • eBook Packages Engineering
  • Print ISBN 978-1-4471-2226-5
  • Online ISBN 978-1-4471-2227-2
  • Series Print ISSN 0178-5354
  • About this book