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Generalized Locally Toeplitz Sequences: Theory and Applications

Volume I

  • Carlo Garoni
  • Stefano Serra-Capizzano

Table of contents

  1. Front Matter
    Pages i-xi
  2. Carlo Garoni, Stefano Serra-Capizzano
    Pages 1-5
  3. Carlo Garoni, Stefano Serra-Capizzano
    Pages 7-43
  4. Carlo Garoni, Stefano Serra-Capizzano
    Pages 45-55
  5. Carlo Garoni, Stefano Serra-Capizzano
    Pages 57-64
  6. Carlo Garoni, Stefano Serra-Capizzano
    Pages 65-93
  7. Carlo Garoni, Stefano Serra-Capizzano
    Pages 95-114
  8. Carlo Garoni, Stefano Serra-Capizzano
    Pages 115-141
  9. Carlo Garoni, Stefano Serra-Capizzano
    Pages 143-164
  10. Carlo Garoni, Stefano Serra-Capizzano
    Pages 165-172
  11. Carlo Garoni, Stefano Serra-Capizzano
    Pages 173-260
  12. Carlo Garoni, Stefano Serra-Capizzano
    Pages 261-263
  13. Carlo Garoni, Stefano Serra-Capizzano
    Pages 265-298
  14. Back Matter
    Pages 299-312

About this book

Introduction

Based on their research experience, the authors propose a reference textbook in two volumes on the theory of generalized locally Toeplitz sequences and their applications. This first volume focuses on the univariate version of the theory and the related applications in the unidimensional setting, while the second volume, which addresses the multivariate case, is mainly devoted to concrete PDE applications.

This book systematically develops the theory of generalized locally Toeplitz (GLT) sequences and presents some of its main applications, with a particular focus on the numerical discretization of differential equations (DEs). It is the first book to address the relatively new field of GLT sequences, which occur in numerous  scientific applications and are especially dominant in the context of DE discretizations. Written for applied mathematicians, engineers, physicists, and scientists who (perhaps unknowingly) encounter GLT sequences in their research, it is also of interest to those working in the fields of Fourier and functional analysis, spectral analysis of DE discretization matrices, matrix analysis, measure and operator theory, numerical analysis and linear algebra. Further, it can be used as a textbook for a graduate or advanced undergraduate course in numerical analysis.

Keywords

Generalized Locally Toeplitz sequences Toeplitz matrices PDE discretization matrices Numerical methods for the discretization of PDEs Tensor (Kronecker) products of matrices Asymptotic singular value and eigenvalue distribution

Authors and affiliations

  • Carlo Garoni
    • 1
  • Stefano Serra-Capizzano
    • 2
  1. 1.University of InsubriaDept. of Science and High Technology University of InsubriaComoItaly
  2. 2.University of InsubriaDept. of Science and High Technology University of InsubriaComoItaly

Bibliographic information

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