Conjugate Gradient Methods for Toeplitz Systems

A list of technical reports, including some abstracts and copies of some full reports may be found at: Object test coverage using finite state machines. September 1995. On balancing workload in a highly mobile environment. August 1995. Error analysis of a partial pivoting method for structured matrices. June 1995. Abstract In this expository paper, we survey some of the latest developments on using precondi-tioned 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. Diierent preconditioners proposed for Toeplitz systems are reviewed. Applications to Toeplitz-related systems arising from partial diierential equations, queueing networks, signal and image processing, integral equations, and time series analysis are given. To appear in SIAM Review.