# An analytical method as a preconditioning modeling for systems of linear equations

## Abstract

In this paper, we propose a simple and practical preconditioner based on the homotopy analysis method. Furthermore, using this modeling, we design an efficient algorithm to solve linear systems. Within the computational framework, convection–diffusion equation candidates are investigated and evaluated. Finally, computational comparisons of the standard methods against preconditioned methods based on experiments are presented which illustrate the merits of the simplicity, power, and effectiveness of the proposed algorithm.

- Authors:

- Islamic Azad University, Department of Applied Mathematics, Lahijan Branch (Iran, Islamic Republic of)

- Publication Date:

- OSTI Identifier:
- 22769364

- 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; ALGORITHMS; DIFFUSION EQUATIONS; ITERATIVE METHODS; MATRICES; SIMULATION

### Citation Formats

```
Saberi Najafi, H., Edalatpanah, S. A., E-mail: saedalatpanah@gmail.com, and Refahisheikhani, A. H.
```*An analytical method as a preconditioning modeling for systems of linear equations*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0376-Y.

```
Saberi Najafi, H., Edalatpanah, S. A., E-mail: saedalatpanah@gmail.com, & Refahisheikhani, A. H.
```*An analytical method as a preconditioning modeling for systems of linear equations*. United States. doi:10.1007/S40314-016-0376-Y.

```
Saberi Najafi, H., Edalatpanah, S. A., E-mail: saedalatpanah@gmail.com, and Refahisheikhani, A. H. Tue .
"An analytical method as a preconditioning modeling for systems of linear equations". United States. doi:10.1007/S40314-016-0376-Y.
```

```
@article{osti_22769364,
```

title = {An analytical method as a preconditioning modeling for systems of linear equations},

author = {Saberi Najafi, H. and Edalatpanah, S. A., E-mail: saedalatpanah@gmail.com and Refahisheikhani, A. H.},

abstractNote = {In this paper, we propose a simple and practical preconditioner based on the homotopy analysis method. Furthermore, using this modeling, we design an efficient algorithm to solve linear systems. Within the computational framework, convection–diffusion equation candidates are investigated and evaluated. Finally, computational comparisons of the standard methods against preconditioned methods based on experiments are presented which illustrate the merits of the simplicity, power, and effectiveness of the proposed algorithm.},

doi = {10.1007/S40314-016-0376-Y},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}

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