Generalized Locally Toeplitz Sequences: Theory and Applications: Volume I

✍ Scribed by Carlo Garoni, Stefano Serra-Capizzano (auth.)

• Publisher: Springer International Publishing
• Year: 2017
• Tongue: English
• Leaves: 316
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xi
Introduction....Pages 1-5
Mathematical Background....Pages 7-43
Singular Value and Eigenvalue Distribution of a Matrix-Sequence....Pages 45-55
Spectral Distribution of Sequences of Perturbed Hermitian Matrices....Pages 57-64
Approximating Classes of Sequences....Pages 65-93
Toeplitz Sequences....Pages 95-114
Locally Toeplitz Sequences....Pages 115-141
Generalized Locally Toeplitz Sequences....Pages 143-164
Summary of the Theory....Pages 165-172
Applications....Pages 173-260
Future Developments....Pages 261-263
Solutions to the Exercises....Pages 265-298
Back Matter....Pages 299-312

✦ Subjects

Numerical Analysis;Linear and Multilinear Algebras, Matrix Theory;Partial Differential Equations