Advertisement

Interpolation of Rational Matrix Functions

  • Joseph A. Ball
  • Israel Gohberg
  • Leiba Rodman

Part of the Operator Theory: Advances and Applications book series (OT, volume 45)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Introduction

    1. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 1-4
  3. Homogeneous Interpolation Problems with Standard Data

    1. Front Matter
      Pages 5-6
    2. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 7-39
    3. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 40-64
    4. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 65-85
    5. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 86-133
    6. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 134-161
    7. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 162-177
    8. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 178-198
    9. Back Matter
      Pages 199-200
  4. Homogeneous Interpolation Problems with Other Forms of Local Data

    1. Front Matter
      Pages 201-201
    2. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 202-208
    3. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 209-212
    4. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 213-223
    5. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 224-234
    6. Back Matter
      Pages 235-235
  5. Subspace Interpolation Problems

    1. Front Matter
      Pages 236-236
    2. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 237-267
    3. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 280-292
    4. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 293-314
    5. Back Matter
      Pages 315-315
  6. Nonhomogeneous Interpolation Problems

    1. Front Matter
      Pages 316-316
    2. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 317-370
    3. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 371-378
    4. Back Matter
      Pages 379-380
  7. Nonhomogeneous Interpolation Problems with Metric Constraints

    1. Front Matter
      Pages 381-381
    2. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 382-424
    3. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 425-433
    4. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 434-456
    5. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 457-486
    6. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 487-499
    7. Back Matter
      Pages 500-504
  8. Applications to Control and Systems Theory

    1. Front Matter
      Pages 505-505
    2. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 506-532
    3. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 533-546
    4. Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 547-559
    5. Back Matter
      Pages 560-561
  9. Back Matter
    Pages 562-605

About this book

Introduction

This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an independent theory. After two years a major part of the first draft was prepared. Then a long period of revising the original draft and introducing recently acquired results and methods followed. There followed a period of polishing and of 25 chapters and the appendix commuting at various times somewhere between Williamsburg, Blacksburg, Tel Aviv, College Park and Amsterdam (sometimes with one or two of the authors).

Keywords

constraint control equation functions Interpolation Mathematica Meromorphic function model Nevanlinna theory operator polynomial presentation Prime stabilization systems theory

Authors and affiliations

  • Joseph A. Ball
    • 1
  • Israel Gohberg
    • 2
  • Leiba Rodman
    • 3
  1. 1.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.School of Mathematical Science, Raymond and Beverly Sackler Faculty of Exact SciencesTel-Aviv UniversityRamat Aviv, Tel-AvivIsrael
  3. 3.Department of MathematicsThe College of William and MaryWilliamsburgUSA

Bibliographic information

Industry Sectors
Biotechnology