Separable Type Representations of Matrices and Fast Algorithms

Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms

  • Yuli Eidelman
  • Israel Gohberg
  • Iulian Haimovici

Part of the Operator Theory: Advances and Applications book series (OT, volume 234)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Basics on Separable, Semi-separable and Quasiseparable Representations of Matrices

    1. Front Matter
      Pages 1-2
    2. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 3-44
    3. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 45-66
    4. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 67-73
    5. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 75-84
    6. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 85-117
    7. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 119-137
    8. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 139-161
  3. Completion of Matrices with Specified Bands

    1. Front Matter
      Pages 163-164
    2. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 165-177
    3. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 179-199
    4. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 201-217
    5. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 219-228
    6. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 229-244
  4. Quasiseparable Representations of Matrices, Descriptor Systems with Boundary Conditions and First Applications

    1. Front Matter
      Pages 245-246
    2. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 247-260
    3. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 261-278
    4. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 279-293
    5. Yuli Eidelman, Israel Gohberg, Iulian Haimovici
      Pages 295-307

About this book

Introduction

This two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work examines algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters.

The first volume consists of four parts. The first part is mainly theoretical in character, introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part, where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part includes factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structures. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike.

Keywords

Completion problems Factorization and inversion Fast algorithms Quasiseparable representations Structured matrices

Authors and affiliations

  • Yuli Eidelman
    • 1
  • Israel Gohberg
    • 2
  • Iulian Haimovici
    • 3
  1. 1.School of Mathematical SciencesTel Aviv University Raymond & Beverly Sackler Faculty of ExaTel AvivIsrael
  2. 2.School of Mathematical SciencesTel Aviv University Raymond & Beverly Sackler Faculty of ExaTel AvivIsrael
  3. 3.School of Mathematical SciencesTel Aviv University Raymond & Beverly Sackler Faculty of ExaTel AvivIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0606-0
  • Copyright Information Springer Basel 2014
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0605-3
  • Online ISBN 978-3-0348-0606-0
  • Series Print ISSN 0255-0156
  • Series Online ISSN 2296-4878
  • About this book