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On convergence of double splitting methods for non-Hermitian positive semidefinite linear systems. (English) Zbl 1204.65033

The results known for double splitting of monotone matrices and for double splitting of Hermitian positive definite matrices are extended to linear systems with a large sparse non-Hermitian positive semidefinite matrix.

A corresponding iterative scheme is spanned by three successive iterations. The iterations converge to a solution of the original problem for any initial guess ${x}^{\left(0\right)}$, ${x}^{\left(1\right)}$, if and only if the spectral radius of the iteration matrix is less then unity. Some convergence conditions are given and the method is applied to a so called generalized saddle point problem. Under suitable assumptions, it is proved that the double splitting iteration process is uniquely convergent.

##### MSC:
 65F10 Iterative methods for linear systems 15B48 Positive matrices and their generalizations; cones of matrices 65F50 Sparse matrices (numerical linear algebra)
##### References:
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