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Generalized Locally Toeplitz Sequences: Theory and Applications

Volume I

Format: Hardback
Publisher: Springer International Publishing AG, Cham, Switzerland
Published: 26th Jun 2017
Dimensions: w 156mm h 234mm d 19mm
Weight: 634g
ISBN-10: 3319536788
ISBN-13: 9783319536781
Barcode No: 9783319536781
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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.

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"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 Marcellan, zbMATH 1376.15002, 2018)