Multistep matrix splitting iteration preconditioning for singular linear systems
For researchers working on numerical linear algebra, this work offers improved preconditioning techniques for solving large sparse singular linear systems, though it is incremental as it extends existing matrix splitting iteration methods.
The paper proposes multistep matrix splitting iterations as preconditioners for Krylov subspace methods to solve singular linear systems, demonstrating through numerical experiments that multistep GSS and HSS iteration preconditioning are more robust and efficient than standard preconditioners for large sparse singular linear systems.
Multistep matrix splitting iterations serve as preconditioning for Krylov subspace methods for solving singular linear systems. The preconditioner is applied to the generalized minimal residual (GMRES) method and the flexible GMRES (FGMRES) method. We present theoretical and practical justifications for using this approach. Numerical experiments show that the multistep generalized shifted splitting (GSS) and Hermitian and skew-Hermitian splitting (HSS) iteration preconditioning are more robust and efficient compared to standard preconditioners for some test problems of large sparse singular linear systems.