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Finite Sections of Band-Dominated Operators
 
Steffen Roch Technische Universität Darmstadt, Darmstadt, Germany
Finite Sections of Band-Dominated Operators
eBook ISBN:  978-1-4704-0501-4
Product Code:  MEMO/191/895.E
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $40.80
Finite Sections of Band-Dominated Operators
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Finite Sections of Band-Dominated Operators
Steffen Roch Technische Universität Darmstadt, Darmstadt, Germany
eBook ISBN:  978-1-4704-0501-4
Product Code:  MEMO/191/895.E
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $40.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1912008; 87 pp
    MSC: Primary 65; Secondary 46; 47;

    The goal of this text is to review recent advances and to present new results in the numerical analysis of the finite sections method for general band and band-dominated operators. The main topics are the stability of the finite sections method and the asymptotic behavior of singular values. The latter topic is closely related with compactness and Fredholm properties of approximation sequences, and the paper can also serve as an introduction into this remarkable field of numerical analysis. Further the author discusses the behavior of approximation numbers, determinants, essential spectra and essential pseudospectra as well as the localization of pseudomodes of finite sections of band-dominated operators.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction: Band-dominated operators
    • 2. Stability
    • 3. Stable regularizability
    • 4. Compactness
    • 5. Fredholmness
    • 6. Essential fractality
    • 7. Applications
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1912008; 87 pp
MSC: Primary 65; Secondary 46; 47;

The goal of this text is to review recent advances and to present new results in the numerical analysis of the finite sections method for general band and band-dominated operators. The main topics are the stability of the finite sections method and the asymptotic behavior of singular values. The latter topic is closely related with compactness and Fredholm properties of approximation sequences, and the paper can also serve as an introduction into this remarkable field of numerical analysis. Further the author discusses the behavior of approximation numbers, determinants, essential spectra and essential pseudospectra as well as the localization of pseudomodes of finite sections of band-dominated operators.

  • Chapters
  • 1. Introduction: Band-dominated operators
  • 2. Stability
  • 3. Stable regularizability
  • 4. Compactness
  • 5. Fredholmness
  • 6. Essential fractality
  • 7. Applications
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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