Global GPBiCGstab(L) method for solving linear matrix equations

Abstract Global Krylov subspace methods are effective iterative solvers for large linear matrix equations. Several Lanczos-type product (LTPMs) solving standard systems of equations have been extended to their global versions. However, the GPBiCGstab( L ) method, which unifies two well-known LTPMs (i.e., BiCGstab( and GPBiCG methods), has developed recently, it shown that this novel method superior convergence when compared conventional LTPMs. In present study, we therefore extend its version. Herein, not only a naive extension original algorithm but also alternative implementation. This variant enables preconditioning technique be applied stably efficiently. Numerical experiments were performed, results demonstrate effectiveness proposed method.