Carlo Garoni, Stefano Serra-Capizzano

Generalized Locally Toeplitz Sequences: Theory and Applications (eBook, PDF)

Volume II

• Format: PDF

Produktbeschreibung

Based on the authors' research experience, this two-volume reference textbook focuses on the theory of generalized locally Toeplitz sequences and its applications. The first volume discusses the univariate version of the theory and the related applications in the unidimensional setting, while this second volume, which addresses the multivariate case, is mainly devoted to concrete PDE applications.

This book systematically develops the multivariate version of the theory of generalized locally Toeplitz (GLT) sequences and presents some of its main applications to the numerical discretization of partial differential equations (PDEs). 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 PDE discretization matrices, matrix analysis, numerical analysis, linear and multilinear algebra. Further, it can be used as a textbook for graduate or advanced undergraduate courses in numerical analysis.

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Produktdetails

• Verlag: Springer Nature Switzerland
• Seitenzahl: 194
• Erscheinungstermin: 8. Dezember 2018
• Englisch
• ISBN-13: 9783030022334
• Artikelnr.: 54736831

Autorenporträt

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 now has a Marie-Curie postdoctoral position at the USI University of Lugano (Switzerland). He has published about 25 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 a Full Professor of Numerical Analysis, Deputy Rector of the University of Insubria (Italy), and a long-term Visiting Professor at Uppsala University (Sweden). He has authored over 200 research papers in different areas of Mathematics, with more than 90 collaborators all over the world, and he has recently won a Prodi Chair Professorship in Nonlinear Analysis at Würzburg University (Germany). He is the founder of the Ph.D. program "Mathematics of Computation" at the University of Insubria's Department of Science and High Technology.

Inhaltsangabe

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

Rezensionen

"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)

"This book can be useful to mathematicians, theoreticians and to applicants involved in numerical methods." (Serge i Grudski i, Mathematical Reviews, March 2, 2020)