Generalized locally Toeplitz sequences: Spectral analysis and applications to discretized partial differential equations
type: Item
instance of: scholarly article
title: Generalized locally Toeplitz sequences: Spectral analysis and applications to discretized partial differential equations
zbMATH Open document ID: 1028.65109
DOI: 10.1016/S0024-3795(02)00504-9
published in: Linear Algebra and its Applications
publication date: 2003-05-25T00:00:00Z
review text: Some generalizations of Toeplitz matrices and sequences thereof are considered: introduced are generalized locally Toeplitz sequences and multilevel locally Toeplitz sequences with the aim to characterize their asymptotic distribution of singular and eigenvalues using weighted multidimensional Szegő formulas. These results are of interest in connection with finite difference approximations of partial differential equations, with integral equations and with general orthogonal polynomials, and continue work done by the Serra Capizzana, Tili, Turtyshnikov and others.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 1915814
zbMATH Keywords: spectral distribution
zbMATH Keywords: multidimensional Szegő formulas
zbMATH Keywords: Toeplitz and locally Toeplitz sequences
zbMATH Keywords: finite differences
zbMATH Keywords: singular values
zbMATH Keywords: Toeplitz matrices
zbMATH Keywords: eigenvalues
zbMATH Keywords: integral equations
zbMATH Keywords: orthogonal polynomials
author: Stefano Serra Capizzano
MaRDI profile type: Publication
cites work: On bilinear forms in Gaussian random variables and Toeplitz matrices
cites work: The Spectral Theory of Toeplitz Operators. (AM-99)
cites work: Introduction to large truncated Toeplitz matrices
cites work: Conjugate Gradient Methods for Toeplitz Systems
cites work: Q4162607
cites work: Fast Preconditioned Conjugate Gradient Algorithms for Wiener–Hopf Integral Equations
cites work: Q3752135
cites work: Q4769223
cites work: Matrix Analysis
cites work: Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients
cites work: The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
cites work: Asymptotic Spectra of Hermitian Block Toeplitz Matrices and Preconditioning Results
cites work: On the distribution of the singular values of Toeplitz matrices
cites work: Q4405392
cites work: The rate of convergence of Toeplitz based PCG methods for second order nonlinear boundary value problems
cites work: Spectral and structural analysis of high precision finite difference matrices for elliptic operators
cites work: Capizzano, Stefano Serra
cites work: Spectral behavior of matrix sequences and discretized boundary value problems
cites work: Distribution results on the algebra generated by Toeplitz sequences: A finite-dimensional approach
cites work: Superlinear Preconditioners for Finite Differences Linear Systems
cites work: Locally X Matrices, Spectral Distributions, Preconditioning, and Applications
cites work: Positive representation formulas for finite difference discretizations of (elliptic) second order PDEs
cites work: A note on the asymptotic spectra of finite difference discretizations of second order elliptic partial differential equations
cites work: On unitarily invariant norms of matrix-valued linear positive operators.
cites work: Extreme singular values and eigenvalues of non-Hermitian block Toeplitz matrices
cites work: Singular values and eigenvalues of non-Hermitian block Toeplitz matrices
cites work: Locally Toeplitz sequences: Spectral properties and applications
cites work: Some results on complex Toeplitz eigenvalues
cites work: Influence of matrix operations on the distribution of eigenvalues and singular values of Toeplitz matrices
cites work: Thin structure of eigenvalue clusters for non-Hermitian Toeplitz matrices
cites work: A unifying approach to some old and new theorems on distribution and clustering
cites work: Spectra of multilevel Toeplitz matrices: Advanced theory via simple matrix relationships
cites work: Asymptotic behavior of block Toeplitz matrices and determinants
cites work: Szegö's limit theorem: The higher-dimensional matrix case
cites work: Asymptotic expansions for pseudodifferential operators on bounded domains
description: scientific article; zbMATH DE number 1915814