A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations
Applied Numerical Mathematics
Asymmetric Hermitian and skew-Hermitian splitting methods for positive definite linear systems
Computers & Mathematics with Applications
On the HSS iteration methods for positive definite Toeplitz linear systems
Journal of Computational and Applied Mathematics
Numerical study on incomplete orthogonal factorization preconditioners
Journal of Computational and Applied Mathematics
Preconditioned AOR iterative methods for M-matrices
Journal of Computational and Applied Mathematics
Optimization of the parameterized Uzawa preconditioners for saddle point matrices
Journal of Computational and Applied Mathematics
An extension of the conjugate residual method to nonsymmetric linear systems
Journal of Computational and Applied Mathematics
On HSS and AHSS iteration methods for nonsymmetric positive definite Toeplitz systems
Journal of Computational and Applied Mathematics
An alternating preconditioner for saddle point problems
Journal of Computational and Applied Mathematics
New choices of preconditioning matrices for generalized inexact parameterized iterative methods
Journal of Computational and Applied Mathematics
The spectral properties of the preconditioned matrix for nonsymmetric saddle point problems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Triangular and skew-symmetric splitting method for numerical solutions of Markov chains
Computers & Mathematics with Applications
Convergence of a generalized MSSOR method for augmented systems
Journal of Computational and Applied Mathematics
The generalized HSS method for solving singular linear systems
Journal of Computational and Applied Mathematics
A new splitting and preconditioner for iteratively solving non-Hermitian positive definite systems
Computers & Mathematics with Applications
Modified parallel multisplitting iterative methods for non-Hermitian positive definite systems
Advances in Computational Mathematics
A practical formula for computing optimal parameters in the HSS iteration methods
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Convergence analysis of the modified Newton-HSS method under the Hölder continuous condition
Journal of Computational and Applied Mathematics
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By further generalizing the concept of Hermitian (or normal) and skew-Hermitian splitting for a non-Hermitian and positive-definite matrix, we introduce a new splitting, called positive-definite and skew-Hermitian splitting (PSS), and then establish a class of PSS methods similar to the Hermitian (or normal) and skew-Hermitian splitting (HSS or NSS) method for iteratively solving the positive-definite systems of linear equations. Theoretical analysis shows that the PSS method converges unconditionally to the exact solution of the linear system, with the upper bound of its convergence factor dependent only on the spectrum of the positive-definite splitting matrix and independent of the spectrum of the skew-Hermitian splitting matrix as well as the eigenvectors of all matrices involved. When we specialize the PSS to block triangular (or triangular) and skew-Hermitian splitting (BTSS or TSS), the PSS method naturally leads to a BTSS or TSS iteration method, which may be more practical and efficient than the HSS and NSS iteration methods. Applications of the BTSS method to the linear systems of block two-by-two structures are discussed in detail. Numerical experiments further show the effectiveness of our new methods.