The GLT class as a generalized Fourier analysis and applications

From MaRDI portal
Publication:854865

DOI10.1016/j.laa.2006.04.012zbMath1109.65032OpenAlexW2019204386MaRDI QIDQ854865

Stefano Serra Capizzano

Publication date: 7 December 2006

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2006.04.012



Related Items

Constructive approach to the monotone rearrangement of functions, Spectral analysis of finite-dimensional approximations of \(1d\) waves in non-uniform grids, Symbol-based preconditioning for Riesz distributed-order space-fractional diffusion equations, Spectral behavior of preconditioned non-Hermitian multilevel block Toeplitz matrices with matrix-valued symbol, Mass concentration in quasicommutators of Toeplitz matrices, Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem, Lusin theorem, GLT sequences and matrix computations: an application to the spectral analysis of PDE discretization matrices, Rectangular GLT sequences, The theory of locally Toeplitz sequences: a review, an extension, and a few representative applications, Toeplitz momentary symbols: definition, results, and limitations in the spectral analysis of structured matrices, Topological foundations of an asymptotic approximation theory for sequences of matrices with increasing size, Spectral Analysis and Multigrid Methods for Finite Volume Approximations of Space-Fractional Diffusion Equations, Spectral Analysis of Saddle-point Matrices from Optimization problems with Elliptic PDE Constraints, Multilevel symmetrized Toeplitz structures and spectral distribution results for the related matrix-sequences, A systematic approach to reduced GLT, The asymptotic properties of the spectrum of nonsymmetrically perturbed Jacobi matrix sequences, Optimizing a multigrid Runge-Kutta smoother for variable-coefficient convection-diffusion equations, On using a zero lower bound on the physical density in material distribution topology optimization, The spectral approximation of multiplication operators via asymptotic (structured) linear algebra, Quasi-optimal preconditioners for finite element approximations of diffusion dominated convection-diffusion equations on (nearly) equilateral triangle meshes, Two-grid optimality for Galerkin linear systems based on B-splines, On the spectrum of stiffness matrices arising from isogeometric analysis, Asymptotic spectra of large (grid) graphs with a uniform local structure. II: Numerical applications, Symbol-Based Multigrid Methods for Galerkin B-Spline Isogeometric Analysis, Approximating classes of sequences: The Hermitian case, Symbol based convergence analysis in multigrid methods for saddle point problems, Distribution results for a special class of matrix sequences: joining approximation theory and asymptotic linear algebra, A note on the (regularizing) preconditioning of \(g\)-Toeplitz sequences via \(g\)-circulants, A sine transform based preconditioned MINRES method for all-at-once systems from constant and variable-coefficient evolutionary PDEs, Spectral analysis and spectral symbol of matrices in isogeometric Galerkin methods, Sequences of variable-coefficient Toeplitz matrices and their singular values, Exploration of Toeplitz-like matrices with unbounded symbols is not a purely academic journey, Spectral and norm estimates for matrix-sequences arising from a finite difference approximation of elliptic operators, Spectral analysis and spectral symbol for the 2D curl-curl (stabilized) operator with applications to the related iterative solutions, Computation of asymptotic spectral distributions for sequences of grid operators, Block Locally Toeplitz Sequences: Construction and Properties, Block Generalized Locally Toeplitz Sequences: Topological Construction, Spectral Distribution Results, and Star-Algebra Structure, Stability of the notion of approximating class of sequences and applications, Schur Complement Matrix and Its (Elementwise) Approximation: A Spectral Analysis Based on GLT Sequences, Fast parallel solver for the space-time IgA-DG discretization of the diffusion equation, Spectral analysis of matrices in Galerkin methods based on generalized B-splines with high smoothness, Spectral asymptotics for Kac-Murdock-Szegő matrices, Spectral distribution results beyond the algebra generated by variable-coefficient Toeplitz sequences: the GLT approach, Tools for the eigenvalue distribution in a non-Hermitian setting, Asymptotic behavior of generalized convolutions: an algebraic approach, The eigenvalue distribution of products of Toeplitz matrices - clustering and attraction, Preconditioned HSS method for large multilevel block Toeplitz linear systems via the notion of matrix‐valued symbol, Banach Spaces of GLT Sequences and Function Spaces, A note on the spectral distribution of symmetrized Toeplitz sequences, Spectral and convergence analysis of the discrete ALIF method, Asymptotic spectra of large (grid) graphs with a uniform local structure. I: Theory, Isogeometric discretizations with generalized B-splines: symbol-based spectral analysis, Space-Time FE-DG Discretization of the Anisotropic Diffusion Equation in Any Dimension: The Spectral Symbol, Spectral analysis and spectral symbol of matrices in isogeometric collocation methods, Spectral analysis and structure preserving preconditioners for fractional diffusion equations, Eigenvalue-eigenvector structure of Schoenmakers-Coffey matrices via Toeplitz technology and applications, Robust and optimal multi-iterative techniques for Iga Galerkin linear systems, Robust and optimal multi-iterative techniques for Iga collocation linear systems, Analysis of the spectral symbol associated to discretization schemes of linear self-adjoint differential 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, Upper Hessenberg and Toeplitz Bohemian matrix sequences: a note on their asymptotical eigenvalues and singular values, Block generalized locally Toeplitz sequences: from the theory to the applications, Spectral analysis of coupled PDEs and of their Schur complements via generalized locally Toeplitz sequences in 2D, An algebraic generalization of local Fourier analysis for grid transfer operators in multigrid based on Toeplitz matrices, Block GLT Sequences: Matrix Functions and Engineering Application, The Eigenvalue Distribution of Special 2-by-2 Block Matrix-Sequences with Applications to the Case of Symmetrized Toeplitz Structures, Spectral analysis of matrices resulting from isogeometric immersed methods and trimmed geometries, Spectral Analysis and Spectral Symbol of $d$-variate $\mathbb Q_{\boldsymbol p}$ Lagrangian FEM Stiffness Matrices


Uses Software


Cites Work