Multigrid methods for Toeplitz linear systems with different size reduction
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Publication:438734
DOI10.1007/s10543-011-0356-yzbMath1251.65047arXiv1010.5730OpenAlexW2056645965MaRDI QIDQ438734
Marco Donatelli, Debora Sesana, Stefano Serra Capizzano
Publication date: 31 July 2012
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1010.5730
convergencenumerical experimentscirculant\(g\)-circulant and Toeplitz matricestwo-grid and multigrid methods
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Iterative numerical methods for linear systems (65F10) Toeplitz, Cauchy, and related matrices (15B05)
Related Items (10)
Sparse matrix approximations for multigrid methods ⋮ A fast and efficient two-grid method for solving \(d\)-dimensional Poisson equations ⋮ Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem ⋮ Toeplitz momentary symbols: definition, results, and limitations in the spectral analysis of structured matrices ⋮ Asymptotic spectra of large (grid) graphs with a uniform local structure. II: Numerical applications ⋮ Mixed two-grid finite difference methods for solving one-dimensional and two-dimensional Fitzhugh-Nagumo equations ⋮ Multigrid methods: grid transfer operators and subdivision schemes ⋮ Symbol approach in a signal-restoration problem involving block Toeplitz matrices ⋮ A note on the eigenvalues of \(g\)-circulants (and of \(g\)-Toeplitz, \(g\)-Hankel matrices) ⋮ Robust and optimal multi-iterative techniques for Iga Galerkin linear systems
Cites Work
- Matrix algebra preconditioners for multilevel Toeplitz systems do not insure optimal convergence rate
- A \(V\)-cycle multigrid for multilevel matrix algebras: proof of optimality
- Comparison of bounds for V-cycle multigrid
- Properties of unilevel block circulants
- Multigrid methods for Toeplitz matrices
- Multi-iterative methods
- Matrix algebra preconditioners for multilevel Toeplitz matrices are not superlinear
- A note on the convergence of the two-grid method for Toeplitz systems
- Multigrid preconditioning and Toeplitz matrices
- Convergence analysis of two-grid methods for elliptic Toeplitz and PDEs matrix-sequences
- Multigrid methods for block Toeplitz matrices with small size blocks
- Algebraic analysis of aggregation-based multigrid
- Spectral Features and Asymptotic Properties for g-Circulants and g-Toeplitz Sequences
- An algebraic generalization of local Fourier analysis for grid transfer operators in multigrid based on Toeplitz matrices
- A superfast solver for real symmetric Toeplitz systems using real trigonometric transformations
- Estimates of inverses of multivariable Toeplitz matrices
- Fast design of multichannel FIR least-squares filters with optimum lag
- Multigrid Method for Ill-Conditioned Symmetric Toeplitz Systems
- V-cycle Optimal Convergence for Certain (Multilevel) Structured Linear Systems
- Multigrid Methods for Multilevel Circulant Matrices
- Any Circulant-Like Preconditioner for Multilevel Matrices Is Not Superlinear
- Conjugate Gradient Methods for Toeplitz Systems
- Multigrid Methods for Symmetric Positive Definite Block Toeplitz Matrices with Nonnegative Generating Functions
- Compact Fourier Analysis for Designing Multigrid Methods
- Convergence of the multigrid method for ill-conditioned block Toeplitz systems
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