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Abstract
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In [1] Bai et al. proposed Hermitian and skew-Hermitian splitting (HSS) iterative method to solve the linear systems Ax = b. They splitted the cofficeint matrix A as A = H + S where H and S are Hermitian and skew-Hermitian part of A, respectively. In [2] Benzi proposed the generalization of the HSS (GHSS) method to solve linear systems. He splitted the Hermitian part of coefficient matrix as H = G + K where G and K are semi-definite matrices. Moreover, Lv et al. presented a special HSS (SHSS) method for image restoration problem in [3]. In our study, we present a splitting for the Hermitian part of the coefficient matrix. The proposed splitting is applied to implement the GHSS method for image restoration problem. The convergence of the method is investigated. Moreover, a special case of the proposed method is also presented for image restoration problem. Two numerical examples are given to show the efficiency and accuracy of the GHSS method and compare proposed method with the SHHS method.
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