Generalized Locally Toeplitz Sequences: Theory and Applications: Volume II

ISBN-13: 9783030022327 / Angielski / Twarda / 2018 / 194 str.

Carlo Garoni; Stefano Serra-Capizzano

Opis

The present book systematically develops the multivariate version of the theory of GLT sequences, also known as the theory of multilevel GLT sequences, and presents some of its main applications in the context of PDE discretizations. Since GLT sequences are a relatively young research field, the book is pioneering in its survey area. It is written for applied mathematicians, engineers, physicists, and scientists who (perhaps unknowingly) encounter GLT sequences in their research. It can also be of interest to researchers working in the fields of Fourier and Functional Analysis, Spectral Analysis of PDE discretization matrices, Matrix Analysis and Matrix Theory, Numerical Analysis, Linear and Multilinear Algebra. The book can be used as a textbook for a graduate-level course in Numerical Analysis.

Recenzje

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

Spis treści

1 Notes to the Reader.- 2 Mathematical Background.- 3 Multilevel Toeplitz Sequences.- 4 Multilevel Locally Toeplitz Sequences.- 5 Multilevel Generalized Locally Toeplitz Sequences.- 6 Summary of the Theory.- 7 Applications.- 8 Future Developments.

O autorze

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.

Blurb

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.