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Conjugate gradient methods for toeplitz systems
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DOI：10.1137/S0036144594276474.png)
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摘要
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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.
Keyword:
Toeplitz matrices
preconditioners
preconditioned conjugate gradient methods
differential equations
signal and image processing
time series
queueing problems
integral equations
期刊
IF:
6.1
论文数:
888
被引数:
1.2W
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