# 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:

- 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}

}

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