A systematic approach to reduced GLT

DOI10.1007/s10543-021-00896-7zbMath1495.15035arXiv2010.03492OpenAlexW3201432236MaRDI QIDQ2162717

Giovanni Barbarino

Publication date: 9 August 2022

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.03492

zbMATH Keywords

asymptotic distributionfinite elementseigenvaluesfinite differencessingular valuesalgebra of sequencesdiscretization of PDEmultilevel generalized locally Toeplitz sequence

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Finite difference methods for boundary value problems involving PDEs (65N06) Multilinear algebra, tensor calculus (15A69) Toeplitz, Cauchy, and related matrices (15B05)

Related Items

Asymptotic spectra of large (grid) graphs with a uniform local structure. II: Numerical applications, An extension of the theory of GLT sequences: sampling on asymptotically uniform grids, Modeling excitable cells with the EMI equations: spectral analysis and iterative solution strategy, Spectral and norm estimates for matrix-sequences arising from a finite difference approximation of elliptic operators, Spectral analysis of matrices resulting from isogeometric immersed methods and trimmed geometries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectral and computational properties of band symmetric Toeplitz matrices
• The GLT class as a generalized Fourier analysis and applications
• The asymptotic properties of the spectrum of nonsymmetrically perturbed Jacobi matrix sequences
• On the distribution of the singular values of Toeplitz matrices
• On bilinear forms in Gaussian random variables and Toeplitz matrices
• Introduction to large truncated Toeplitz matrices
• The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
• Locally Toeplitz sequences: Spectral properties and applications
• Spectra of multilevel Toeplitz matrices: Advanced theory via simple matrix relationships
• Generalized locally Toeplitz sequences: Spectral analysis and applications to discretized partial differential equations
• A general equidistribution theorem for the roots of orthogonal polynomials
• A unifying approach to some old and new theorems on distribution and clustering
• Asymptotic spectra of large (grid) graphs with a uniform local structure. I: Theory
• Computation of asymptotic spectral distributions for sequences of grid operators
• Block generalized locally Toeplitz sequences: theory and applications in the unidimensional case
• Block generalized locally Toeplitz sequences: theory and applications in the multidimensional case
• Equivalence between GLT sequences and measurable functions
• Generalized Locally Toeplitz Sequences: Theory and Applications
• Spectral Measures
• Non‐Hermitian perturbations of Hermitian matrix‐sequences and applications to the spectral analysis of the numerical approximation of partial differential equations
• Distribution of eigenvalues and singular values of Toeplitz matrices under weakened conditions on the generating function
• From convergence in measure to convergence of matrix-sequences through concave functions and singular values
• Superlinear Preconditioners for Finite Differences Linear Systems
• A note on the spectral distribution of toeplitz matrices
• Generalized Locally Toeplitz Sequences: Theory and Applications
• On the Asymptotic Spectrum of Finite Element Matrix Sequences
• Extreme Eigenvalues of Translation Kernels
• Spectral Properties of Banded Toeplitz Matrices
• The Numerical Solution of Laplace's Equation
• Some remarks on the measurability of certain sets
• Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients