ANU Computer Science Technical Reports

TR-CS-95-07

Raymond H. Chan and Michael K. Ng.
Conjugate gradient methods for Toeplitz systems.
September 1995.
To appear in SIAM review.

[POSTSCRIPT (489123 bytes)] [PDF (601785 bytes)]

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 differential equations, queueing networks, signal and image processing, integral equations, and time series analysis are given.

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