Conjugate Gradient Methods for Toeplitz Systems
SIAM Review
Effective Methods for Solving Banded Toeplitz Systems
SIAM Journal on Matrix Analysis and Applications
Circulant preconditioners for solving ordinary differential equations
Structured matrices
A Circulant Preconditioner for the Systems of LMF-Based ODE Codes
SIAM Journal on Scientific Computing
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We consider the solution of ordinary differential equations (ODEs) using implicit linear multistep formulae (LMF). More precisely, here we consider Boundary Value Methods. These methods require the solution of one or more unsymmetric, large and sparse linear systems. I n [6], Chan et al. proposed using Strang block-circulant preconditioners for solving these linear systems. However, as observed in [1], Strang preconditioners can be often ill-conditioned or singular even when the given system is well-conditioned. In this paper, we propose a nonsingular skew-circulant preconditioner for systems of LMF-based ODE codes. Numerical results are given to illustrate the effectiveness of our method.