A Fast MAP Algorithm for High-Resolution Image Reconstruction with Multisensors
Multidimensional Systems and Signal Processing
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Circulant-block preconditioners for solving ordinary differential equations
Applied Mathematics and Computation
Negative Results for Multilevel Preconditioners in Image Deblurring
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
Skew-Circulant Preconditioners for Systems of LMF-Based ODE Codes
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
A Fast Algorithm for High-Resolution Color Image Reconstruction with Multisensors
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Preliminary Remarks on Multigrid Methods for Circulant Matrices
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
A note on the fast algorithm for block Toeplitz systems with tensor structure
Applied Mathematics and Computation
Nyström-Clenshaw-Curtis quadrature for integral equations with discontinuous kernels
Mathematics of Computation
Fast unified computation of the multi-dimensional discrete sinusoidal transforms
Applied Mathematics and Computation
HPC-ASIA '97 Proceedings of the High-Performance Computing on the Information Superhighway, HPC-Asia '97
Nonlinear image restoration using FFT-based conjugate gradient methods
ICIP '95 Proceedings of the 1995 International Conference on Image Processing (Vol.2)-Volume 2 - Volume 2
How to prove that a preconditioner cannot be superlinear
Mathematics of Computation
Circulant and skew-circulant splitting methods for Toeplitz systems
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 6th Japan--China joint seminar on numerical mathematics, university of Tsukuba, Japan, 5-9 August 2002
Circulant preconditioned WR-BVM methods for ODE systems
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Preconditioned WR-LMF-based method for ODE systems
Journal of Computational and Applied Mathematics
Fast inversion of triangular Toeplitz matrices
Theoretical Computer Science - Algebraic and numerical algorithm
Theoretical Computer Science - Algebraic and numerical algorithm
Super-Resolution Image Restoration from Blurred Low-Resolution Images
Journal of Mathematical Imaging and Vision
Semi-supervised nonlinear dimensionality reduction
ICML '06 Proceedings of the 23rd international conference on Machine learning
Boundary conditions and multiple-image re-blurring: the LBT case
Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
Regularized fast multiple-image deconvolution for LBT
Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
Super-resolution reconstruction based on linear interpolation of wavelet coefficients
Multidimensional Systems and Signal Processing
Multigrid solution techniques for anisotropic structured linear systems
Applied Numerical Mathematics
Journal of Computational Physics
Stability of the notion of approximating class of sequences and applications
Journal of Computational and Applied Mathematics
Fredholm integral equation method for the integro-differential Schrödinger equation
Computers & Mathematics with Applications
On the HSS iteration methods for positive definite Toeplitz linear systems
Journal of Computational and Applied Mathematics
Non-negatively constrained image deblurring with an inexact interior point method
Journal of Computational and Applied Mathematics
A modified T. Chan's preconditioner for Toeplitz systems
Computers & Mathematics with Applications
Block preconditioners with circulant blocks for general linear systems
Computers & Mathematics with Applications
BCCB preconditioners for solving linear systems from delay differential equations
Computers & Mathematics with Applications
A direct method to solve block banded block Toeplitz systems with non-banded Toeplitz blocks
Journal of Computational and Applied Mathematics
On HSS and AHSS iteration methods for nonsymmetric positive definite Toeplitz systems
Journal of Computational and Applied Mathematics
Applications of FFT and structured matrices
Algorithms and theory of computation handbook
Another Constructed Chaotic Image Encryption Scheme Based on Toeplitz Matrix and Hankel Matrix
Fundamenta Informaticae
Journal of Computational and Applied Mathematics
Iterative Solvers for the Stochastic Finite Element Method
SIAM Journal on Scientific Computing
Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential
SIAM Journal on Scientific Computing
Approximate Inverse Circulant-plus-Diagonal Preconditioners for Toeplitz-plus-Diagonal Matrices
SIAM Journal on Scientific Computing
Antireflective boundary conditions for deblurring problems
Journal of Electrical and Computer Engineering - Special issue on iterative signal processing in communications
A Novel Circulant Approximation Method for Frequency Domain LMMSE Equalization
Journal of Signal Processing Systems
A composite preconditioner for the electromagnetic scattering from a large cavity
Journal of Computational Physics
Multigrid method for fractional diffusion equations
Journal of Computational Physics
A note on the (regularizing) preconditioning of g-Toeplitz sequences via g-circulants
Journal of Computational and Applied Mathematics
A new preconditioner for the interface system arising in a fast Helmholtz solver
Computers & Mathematics with Applications
BTTB preconditioners for BTTB systems
Numerical Algorithms
Journal of Computational Physics
Tri-diagonal preconditioner for pricing options
Journal of Computational and Applied Mathematics
A circulant preconditioner for fractional diffusion equations
Journal of Computational Physics
Preconditioned iterative methods for fractional diffusion equation
Journal of Computational Physics
A generalization of the optimal diagonal approximate inverse preconditioner
Computers & Mathematics with Applications
Journal of Computational Physics
New preconditioners for systems of linear equations with Toeplitz structure
Calcolo: a quarterly on numerical analysis and theory of computation
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In this expository paper, we survey some of the latest developments in using preconditioned conjugate gradient methods for solving Toeplitz systems. One of the main results is that the complexity of solving a large class of $n$-by-$n$ Toeplitz systems is reduced to $O(n \log n)$ operations as compared to $O(n \log ^2 n)$ operations required by fast direct Toeplitz solvers. Different preconditioners proposed for Toeplitz systems are reviewed. Applications to Toeplitz-related systems arising from partial differential equations, queueing networks, signal and image processing, integral equations, and time series analysis are given.