Generalized Locally Toeplitz Sequences: Theory and Applications

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 has now a Marie-Curie postdoctoral position at the USI University of Lugano (Switzerland). He has published around 20 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 full professor in numerical analysis at the University of Insubria (Italy), head of the Department of Science and High Technology at the same university, and long-term visiting professor at the Department of Information Technology at Uppsala University (Sweden). He has authored over 170 research papers in different areas of mathematics, with more than 70 collaborators all over the world. He is the founder of the Ph.D. Program “Mathematics ofComputation” at the University of Insubria.

“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)

• 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