The solution of ill-conditioned symmetric Toeplitz systems via two-grid and wavelet methods

DOI10.1016/S0898-1221(03)90142-8zbMath1051.65030OpenAlexW1984454101MaRDI QIDQ597322

Zenghui Zhang, Li-Zhi Cheng, Hong-Xia Wang

Publication date: 6 August 2004

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0898-1221(03)90142-8

zbMATH Keywords

convergencenumerical experimentstwo-grid methoddamped-Jacobi iterationill-conditioned symmetric Toeplitz matricesWavelet filter

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Numerical methods for wavelets (65T60) Iterative numerical methods for linear systems (65F10)

Related Items

Fast wavelet transform for Toeplitz matrices and property analysis ⋮ An algebraic generalization of local Fourier analysis for grid transfer operators in multigrid based on Toeplitz matrices ⋮ Generalized grid transfer operators for multigrid methods applied on Toeplitz matrices

Cites Work

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• A note on the convergence of the two-grid method for Toeplitz systems
• Preconditioners for Ill-Conditioned Toeplitz Systems Constructed from Positive Kernels
• A theory for multiresolution signal decomposition: the wavelet representation
• Biorthogonal bases of compactly supported wavelets
• Superlinear PCG methods for symmetric Toeplitz systems
• How to Choose the Best Iterative Strategy for Symmetric Toeplitz Systems
• The Lifting Scheme: A Construction of Second Generation Wavelets
• Multigrid Method for Ill-Conditioned Symmetric Toeplitz Systems
• A new class of biorthogonal wavelet systems for image transform coding
• The Best Circulant Preconditioners for Hermitian Toeplitz Systems
• Conjugate Gradient Methods for Toeplitz Systems
• Multigrid Methods for Symmetric Positive Definite Block Toeplitz Matrices with Nonnegative Generating Functions