VPAStab(): An iterative method with look-ahead for the solution of large sparse linear systems

VPAStab(J,L) denotes an iterative method designed to give an accurate numerical solution of a large sparse system of linear equations. The iteration comprises L-steps and possibly jump-steps. An L-step involves stabilisation (minimisation) over an L-dimensional subspace following L levels of vector-Padé approximation. A jump-step (look-ahead stage) avoids near-breakdowns by jumping past them by J levels simultaneously. A numerical implementation of VPAStab(2,L) is considered in the context of some well-known examples.