Separable Type Representations of Matrices and Fast Algorithms

Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms

Authors:

ISBN: 978-3-0348-0605-3 (Print) 978-3-0348-0606-0 (Online)

Table of contents (20 chapters)

  1. Front Matter

    Pages i-xv

  2. Basics on Separable, Semi-separable and Quasiseparable Representations of Matrices

    1. Front Matter

      Pages 1-2

    2. No Access

      Book Chapter

      Pages 3-44

      Matrices with Separable Representation and Low Complexity Algorithms

    3. No Access

      Book Chapter

      Pages 45-66

      The Minimal Rank Completion Problem

    4. No Access

      Book Chapter

      Pages 67-73

      Matrices in Diagonal Plus Semiseparable Form

    5. No Access

      Book Chapter

      Pages 75-84

      Quasiseparable Representations: The Basics

    6. No Access

      Book Chapter

      Pages 85-117

      Quasiseparable Generators

    7. No Access

      Book Chapter

      Pages 119-137

      Rank Numbers of Pairs of Mutually Inverse Matrices, Asplund Theorems

    8. No Access

      Book Chapter

      Pages 139-161

      Unitary Matrices with Quasiseparable Representations

  3. Completion of Matrices with Specified Bands

    1. Front Matter

      Pages 163-164

    2. No Access

      Book Chapter

      Pages 165-177

      Completion to Green Matrices

    3. No Access

      Book Chapter

      Pages 179-199

      Completion to Matrices with Band Inverses and with Minimal Ranks

    4. No Access

      Book Chapter

      Pages 201-217

      Completion of Special Types of Matrices

    5. No Access

      Book Chapter

      Pages 219-228

      Completion of Mutually Inverse Matrices

    6. No Access

      Book Chapter

      Pages 229-244

      Completion to Unitary Matrices

  4. Quasiseparable Representations of Matrices, Descriptor Systems with Boundary Conditions and First Applications

    1. Front Matter

      Pages 245-246

    2. No Access

      Book Chapter

      Pages 247-260

      Quasiseparable Representations and Descriptor Systems with Boundary Conditions

    3. No Access

      Book Chapter

      Pages 261-278

      The First Inversion Algorithms

    4. No Access

      Book Chapter

      Pages 279-293

      Inversion of Matrices in Diagonal Plus Semiseparable Form

    5. No Access

      Book Chapter

      Pages 295-307

      Quasiseparable/Semiseparable Representations and One-direction Systems

    6. No Access

      Book Chapter

      Pages 309-326

      Multiplication of Matrices

  5. Factorization and Inversion

    1. Front Matter

      Pages 327-328

    2. No Access

      Book Chapter

      Pages 329-351

      The LDU Factorization and Inversion

    3. No Access

      Book Chapter

      Pages 353-372

      Scalar Matrices with Quasiseparable Order One

    4. No Access

      Book Chapter

      Pages 373-391

      The QR-Factorization Based Method

  6. Back Matter

    Pages 393-399