Recycling BiCGSTAB with an Application to Parametric Model Order Reduction

TLDR: In this article, the recycling BiCG algorithm is extended to BiCGSTAB, which uses a recycle space, which is built from left and right approximate invariant subspaces.

Abstract: Krylov subspace recycling is a process for accelerating the convergence of sequences of linear systems. Based on this technique, the recycling BiCG algorithm has been developed recently. Here, we now generalize and extend this recycling theory to BiCGSTAB. Recycling BiCG focuses on efficiently solving sequences of dual linear systems, while the focus here is on efficiently solving sequences of single linear systems (assuming nonsymmetric matrices for recycling BiCG and recycling BiCGSTAB). As compared with other methods for solving sequences of single linear systems with nonsymmetric matrices (e.g., recycling variants of GMRES), BiCG-based recycling algorithms, like recycling BiCGSTAB, have the advantage that they involve a short-term recurrence and hence do not suffer from storage issues and are also cheaper with respect to the orthogonalizations. We modify the BiCGSTAB algorithm to use a recycle space, which is built from left and right approximate invariant subspaces. Using our algorithm for a parametr...