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Conjugate Gradient Methods for Toeplitz Systems
Open accessAbstract
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.
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Cites
An algorithm for the machine calculation of complex Fourier series
Cooley, J. W., & Tukey, J. W. (1965) · Mathematics of Computation · doi:10.1090/s0025-5718-1965-0178586-1 · Cited by 13,154
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Candès, E., Demanet, L., Donoho, D., & Ying, L. (2006) · Multiscale Modeling & Simulation · doi:10.1137/05064182x · Cited by 2,573
Fast, robust total variation-based reconstruction of noisy, blurred images
Vogel, C. R., & Oman, M. E. (1998) · IEEE Transactions on Image Processing · doi:10.1109/83.679423 · Cited by 601
An Order-$p$ Tensor Factorization with Applications in Imaging
Martin, C. D., Shafer, R., & LaRue, B. (2013) · SIAM Journal on Scientific Computing · doi:10.1137/110841229 · Cited by 296
Metadata
- Authors
- Chan, R. H., & Ng, M. K.
- Venue
- SIAM Review
- Published
- 1996-09
- Volume
- 38
- Issue
- 3
- Pages
- 427-482
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2005041367
- Cited by
- 801
- References
- 1
- FWCI
- 28.34
- Type
- journal article
- Language
- en
- Open access
- green
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