The generalized HSS method for solving singular linear systems
The authors present a new GHSS (generalized Hermitian and skew--Hermitian splitting) method for an iterative solution of the large, sparse, non-Hermitian and singular linear system. They derive the GHSS method starting with a Hermitian and skew-Hermitian splitting of the matrix of the system. This splitting depends on two parameters, while the HSS method uses only one parameter-splitting. The advantage of the GHSS method is that as a result of the splitting it can naturally induce a preconditioner that improve the convergence rate of GMRES. On the other hand, costs less time to converge than GHSS. The authors give and prove sufficient conditions for the GHSS method to be semi-convergent and analyze the quasi-optimal choice of the parameters. Numerical examples are included and the results are discussed.
non-Hermitian and singular linear system
scientific article; zbMATH DE number 6015748
scientific article