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Generalized Locally Toeplitz Sequences: Theory and Applications

Volume I

Authors: Garoni, Carlo, Serra-Capizzano, Stefano

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  • - Introduces readers into the world of GLT sequences and their applications
  • - Offers several applications with illustrations and numerical examples that help readers become familiar with GLT sequences
  • -  Includes a concise summary of the theory of GLT sequences that allows readers to skip the full theory on first reading
  • -  Contains the solutions to all the proposed exercises
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About this book

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.

About the authors

Dr. Carlo Garoni graduated in mathematics at the University of Insubria (Italy) in 2011 and received his Ph.D. in mathematics at the same university in 2015. He has pursued research at the Universities of Insubria and Rome “Tor Vergata”, and he has now a Marie-Curie postdoctoral position at the USI University of Lugano (Switzerland). He has published around 20 research papers in different areas of mathematics, most of which are connected with the theory of GLT sequences and its applications.

Prof. Stefano Serra-Capizzano is full professor in numerical analysis at the University of Insubria (Italy), head of the Department of Science and High Technology at the same university, and long-term visiting professor at the Department of Information Technology at Uppsala University (Sweden). He has authored over 170 research papers in different areas of mathematics, with more than 70 collaborators all over the world. He is the founder of the Ph.D. Program “Mathematics of Computation” at the University of Insubria.

Reviews

“The authors deal with the analysis of the spectral and singular value distribution of sequences of matrices related with Toeplitz matrices, as well as the so-called locally Toeplitz and generalized locally Toeplitz matrices, which appear in the discretization of boundary value problems for linear differential equations when finite difference methods and finite element methods are used.  … The presentation of the book is very friendly for any reader interested both in computational methods and perturbations of Toeplitz matrices.” (Francisco Marcellán, zbMATH 1376.15002, 2018)

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-319-53679-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-319-53678-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-3-319-85214-0
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Generalized Locally Toeplitz Sequences: Theory and Applications
Book Subtitle
Volume I
Authors
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-53679-8
DOI
10.1007/978-3-319-53679-8
Hardcover ISBN
978-3-319-53678-1
Softcover ISBN
978-3-319-85214-0
Edition Number
1
Number of Pages
XI, 312
Number of Illustrations
16 illustrations in colour
Topics

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