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Abstract: In this expository paper, we survey some of the latest developments on 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... (Update)
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BibTeX entry: (Update)
R. Chan and M. Ng, "Conjugate gradient methods for Toeplitz systems", SIAM Review 38, pp. 427--482, 1996. http://citeseer.ist.psu.edu/article/chan96conjugate.html More
@article{ chan96conjugate,
author = "Raymond H. Chan and Michael K. Ng",
title = "Conjugate Gradient Methods for {Toeplitz} Systems",
journal = "SIAM Review",
volume = "38",
number = "3",
pages = "427--482",
year = "1996",
url = "citeseer.ist.psu.edu/article/chan96conjugate.html" }
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3 Preconditioners for Wiener-Hopf Equations with Higher Order .. - Lin, Ng et al.
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3 Preconditioned Iterative Methods for Solving Toeplitz-plus-H.. (context) - Ku, Kuo - 1993
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2 Fast FFT-based Conjugate Gradient Algorithm for Applications.. (context) - Ng - 1993
2 The Toeplitz-Circulant Eigenvalue Problem Ax = Cx (context) - Strang, Edelman - 1987
2 Circulant Integral Operators and Circulant Preconditioners (context) - Chan, Lin - 1993
2 Signal Processing and Systems Theory (context) - Chui, Chen - 1992
2 Adaptive Signal Processing (context) - Sibul - 1987
2 Extended Circulant Conditioning of Toeplitz Systems (context) - Linzer - 1992
2 On Circulant Preconditioning of Elliptic Problems in L-shape.. (context) - Lirkov, Margenov - 1994
2 Hartley Preconditioners for Toeplitz Systems Generated by Po.. (context) - Jin - 1994
2 Band-Toeplitz Preconditioners for Block Toeplitz Systems (context) - Jin
2 Optimal Circulant Preconditioning for Arbitrary Matrices (context) - Sayed, Kailath
2 Which Circulant Preconditioners are Better (context) - Tyrtyshnikov, Strela
1 the Algebraic Structure of the Spaces of Toeplitz and Hankel.. (context) - Pusty, On - 1980
1 Englewood Cliiffs (context) - Hamming, Filters et al. - 1989
1 Approximation Thoery and Numerical Linear Algebra (context) - Trefethen - 1990
1 Plemmons Fast Recursive Least Squares Using the FFT (context) - Ng - 1994
1 Iterative Method for Solving Toeplitz-plus-Hankel Least Squa.. (context) - Ng - 1994
1 Analysis of Semi-Toeplitz Preconditioners for First-order PD.. (context) - Semi, for et al.
1 Zur Theorie der quadratischen und bilinearen Formen von unen.. (context) - Otto - 1911
1 Circulant Integral Operators for Wiener-Hopf Equations (context) - Chan, Jin et al. - 1995
1 Fast Algorithms for Structured Matrices Arbitrary Rank Profi.. (context) - Pal - 1990
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