Conjugate Gradient Methods for Toeplitz Systems

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 u...

Parallelizing the Conjugate Gradient Algorithm for Multilevel Toeplitz Systems

Multilevel Toeplitz linear systems appear in a wide range of scientific and engineering applications. While several fast direct solvers exist for the basic 1-level Toeplitz matrices, in the multilevel case an iterative solver provides the most general and practical solution. Furthermore, iterative methods are asymptotically faster than many stable direct methods even for the 1-level case. This ...

Accurate conjugate gradient methods for shifted systems

We present an efficient and accurate variant of the conjugate gradient method for solving families of shifted systems. In particular we are interested in shifted systems that occur in Tikhonov regularization for inverse problems since these problems can be sensitive to roundoff errors. The success of our method in achieving accurate approximations is supported by theoretical arguments as well a...

Multilevel Conjugate Gradient Methods

Multigrid-Conjugate Gradient Type Methods for Reaction-diffusion Systems

We study multigrid methods in the context of continuation methods for reaction–diffusion systems, where the Bi-CGSTAB and GMRES methods are used as the relaxation scheme for the V-cycle, W-cycle and full approximation schemes, respectively. In particular, we apply the results of Brown and Walker [1997] to investigate how the GMRES method can be used to solve nearly singular systems that occur i...