Abstract
An efficient Hermitian and skew-Hermitian splitting method is presented for solving non-Hermitian and normal positive definite linear systems with strong Hermitian parts. We theoretically prove that this method converges to the unique solution of the system of linear equations. Inexact version of the method which employs conjugate gradient as its inner process is presented. Moreover, we derive an upper bound of the contraction factor of the method. Numerical examples from the finite-difference discretization of a second-order partial differential equation are used to further examine the effectiveness and robustness of both exact and inexact iterations.
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Noormohammadi Pour, H., Sadeghi Goughery, H. New Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems. Numer Algor 69, 207–225 (2015). https://doi.org/10.1007/s11075-014-9890-4
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DOI: https://doi.org/10.1007/s11075-014-9890-4