Separable Type Representations of Matrices and Fast Algorithms

Volume 2 Eigenvalue Method

Authors:

ISBN: 978-3-0348-0611-4 (Print) 978-3-0348-0612-1 (Online)

Table of contents (16 chapters)

  1. Front Matter

    Pages i-xi

  2. The Eigenvalue Structure of Order One Quasiseparable Matrices

    1. Front Matter

      Pages 1-2

    2. No Access

      Book Chapter

      Pages 3-12

      Quasiseparable of Order One Matrices.Characteristic Polynomials

    3. No Access

      Book Chapter

      Pages 13-31

      Eigenvalues with Geometric Multiplicity One

    4. No Access

      Book Chapter

      Pages 33-49

      Kernels of Quasiseparable of Order One Matrices

    5. No Access

      Book Chapter

      Pages 51-71

      Multiple Eigenvalues

  3. Divide and Conquer Method for the Eigenproblem

    1. Front Matter

      Pages 73-74

    2. No Access

      Book Chapter

      Pages 75-93

      Divide Step

    3. No Access

      Book Chapter

      Pages 95-101

      Conquer Step and Eigenproblem for Rational Matrix Functions

    4. No Access

      Book Chapter

      Pages 103-115

      Complete Algorithm for Hermitian Matrices

    5. No Access

      Book Chapter

      Pages 117-131

      Complete Algorithm for Unitary Hessenberg Matrices

  4. Algorithms for QR Iterations and for Reduction to Hessenberg Form

    1. Front Matter

      Pages 133-134

    2. No Access

      Book Chapter

      Pages 135-162

      The QR Iteration Method for Eigenvalues

    3. No Access

      Book Chapter

      Pages 163-205

      The Reduction to Hessenberg Form

    4. No Access

      Book Chapter

      Pages 207-255

      The Implicit QR Iteration Method for Eigenvalues of Upper Hessenberg Matrices

  5. QR Iterations for Companion Matrices

    1. Front Matter

      Pages 257-258

    2. No Access

      Book Chapter

      Pages 259-279

      Companion and Unitary Matrices

    3. No Access

      Book Chapter

      Pages 281-294

      Explicit Methods

    4. No Access

      Book Chapter

      Pages 295-303

      Implicit Methods with Compression

    5. No Access

      Book Chapter

      Pages 305-321

      The Factorization Based Implicit Method

    6. No Access

      Book Chapter

      Pages 323-354

      Implicit Algorithms Based on the QR Representation

  6. Back Matter

    Pages 355-359