Generalized Locally Toeplitz Sequences: Theory and Applications : Volume I / by Carlo Garoni, Stefano Serra-Capizzano.

Format:

Book

Author/Creator:

Garoni, Carlo., Author.

Serra-Capizzano, Stefano., Author.

Language:

English

Subjects (All):

Numerical analysis.

Matrix theory.

Algebra.

Differential equations, Partial.

Numerical Analysis.

Linear and Multilinear Algebras, Matrix Theory.

Partial Differential Equations.

Local Subjects:

Numerical Analysis.

Linear and Multilinear Algebras, Matrix Theory.

Partial Differential Equations.

Physical Description:

1 online resource (XI, 312 p. 16 illus. in color.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

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:

1 Introduction

2 Mathematical background

3 Singular value and eigenvalue distribution of a matrix-sequence

4 Spectral distribution of sequences of perturbed Hermitian matrices

5 Approximating classes of sequences

6 Toeplitz sequences

7 Locally Toeplitz sequences

8 Generalized locally Toeplitz sequences

9 Summary

10 Applications

Future developments

Solutions to the exercises .

Notes:

Includes bibliographical references and index.

ISBN:

3-319-53679-6