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Splitting iteration methods for non-Hermitian positive definite systems of linear equations. (English) Zbl 1138.65027

Summary: For large sparse system of linear equations with a non-Hermitian positive definite coefficient matrix, we review the recently developed Hermitian/skew-Hermitian splitting iteration, normal/skew-Hermitian splitting iteration, positive-definite/skew-Hermitian splitting iteration, and block triangular/skew-Hermitian splitting iteration. These methods converge unconditionally to the exact solution of the linear system, with the upper bounds of their convergence factors being only dependent on the spectrum of the Hermitian (or normal, or positive-definite) splitting matrix, but independent of the spectrum of the skew-Hermitian splitting matrix as well as the eigenvectors of all matrices involved.

MSC:

65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
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