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Title: A special generalized HSS method for discrete ill-posed problems

Abstract

In this paper, we use a new special generalized Hermitian and skew-Hermitian splitting (SGHSS) method for solving ill-posed inverse problems. Based on an augmented system formulation, we apply a new splitting for the Hermitian part of the coefficient matrix and discuss on the convergence of this iterative method. Moreover, the optimal parameter minimizing the spectral radius of iteration matrix is derived. Finally, we present some numerical examples to demonstrate the performance of the presented method.

Authors:
;  [1]
  1. University of Guilan, Department of Applied Mathematics and Computer Sciences, Faculty of Mathematical Sciences (Iran, Islamic Republic of)
Publication Date:
OSTI Identifier:
22769341
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; ITERATIVE METHODS; MATRICES; PERFORMANCE

Citation Formats

Aminikhah, H., E-mail: hossein.aminikhah@gmail.com, E-mail: aminikhah@guilan.ac.ir, and Yousefi, M., E-mail: mahsa.yousefi1987@gmail.com. A special generalized HSS method for discrete ill-posed problems. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0408-7.
Aminikhah, H., E-mail: hossein.aminikhah@gmail.com, E-mail: aminikhah@guilan.ac.ir, & Yousefi, M., E-mail: mahsa.yousefi1987@gmail.com. A special generalized HSS method for discrete ill-posed problems. United States. doi:10.1007/S40314-016-0408-7.
Aminikhah, H., E-mail: hossein.aminikhah@gmail.com, E-mail: aminikhah@guilan.ac.ir, and Yousefi, M., E-mail: mahsa.yousefi1987@gmail.com. Tue . "A special generalized HSS method for discrete ill-posed problems". United States. doi:10.1007/S40314-016-0408-7.
@article{osti_22769341,
title = {A special generalized HSS method for discrete ill-posed problems},
author = {Aminikhah, H., E-mail: hossein.aminikhah@gmail.com, E-mail: aminikhah@guilan.ac.ir and Yousefi, M., E-mail: mahsa.yousefi1987@gmail.com},
abstractNote = {In this paper, we use a new special generalized Hermitian and skew-Hermitian splitting (SGHSS) method for solving ill-posed inverse problems. Based on an augmented system formulation, we apply a new splitting for the Hermitian part of the coefficient matrix and discuss on the convergence of this iterative method. Moreover, the optimal parameter minimizing the spectral radius of iteration matrix is derived. Finally, we present some numerical examples to demonstrate the performance of the presented method.},
doi = {10.1007/S40314-016-0408-7},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 2,
volume = 37,
place = {United States},
year = {2018},
month = {5}
}