GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Matrix computations (3rd ed.)
Experimental study of ILU preconditioners for indefinite matrices
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
SIAM Journal on Matrix Analysis and Applications
Iterative solution of linear systems in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Preconditioner for Generalized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems
SIAM Journal on Scientific Computing
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In this paper, efficient iterative methods for the large sparse non-Hermitian positive definite systems of linear equations, based on the Hermitian and skew-Hermitian splitting of the coefficient matrix, are studied. These methods include an asymmetric Hermitian/skew-Hermitian (AHSS) iteration and its inexact version, the inexact asymmetric Hermitian/skew-Hermitian (IAHSS) iteration, which employs some Krylov subspace methods as its inner process. We theoretically study the convergence properties of the AHSS method and the IAHSS method. Moreover, the contraction factor of the AHSS iteration is derived. Numerical examples illustrating the effectiveness of both AHSS and IAHSS iterations are presented.