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Garoni C., Serra-Capizzano S. Generalized Locally Toeplitz Sequences: Theory and Applications. Volume I

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Garoni C., Serra-Capizzano S. Generalized Locally Toeplitz Sequences: Theory and Applications. Volume I
Springer International Publishing AG, 2017. — 316 p. — ISBN 3319536788.
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.
Contents
Introduction
Mathematical Background
Singular Value and Eigenvalue Distribution of a Matrix-Sequence
Spectral Distribution of Sequences of Perturbed Hermitian Matrices
Approximating Classes of Sequences
Toeplitz Sequences
Locally Toeplitz Sequences
Generalized Locally Toeplitz Sequences
Summary of the Theory
Applications
Future Developments
Solutions to the Exercises
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