Advances in the Hybrid Bi-CG Methods for Linear Systems

Abstract

Large sparse linear systems frequently arise in many fields of scientific computing, and therefore, fast and accurate numerical iterative solvers, such as Krylov subspace methods, have been studied in detail over the years. In particular, the hybrid bi-conjugate gradient (Bi-CG) methods belonging to the Krylov subspace methods are extensively used for solving nonsymmetric systems. In the present paper, we introduce basic concepts and recent advances in the hybrid Bi-CG methods, focusing on stabilizing polynomials that distinguish between specific algorithms.