# On LPMHSS-based iteration methods for a class of weakly nonlinear systems

## Abstract

In this paper, for a class of the large sparse system of weakly nonlinear equations, combining separable property of the linear and nonlinear terms with the lopsided Hermitian and skew-Hermitian splitting (LHSS) of the coefficient matrix, the Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are presented. Theoretical analysis shows that these methods are locally convergent under suitable conditions. Numerical results show that both Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are feasible and effective for the large-scale system of weakly nonlinear equations.

- Authors:

- Anyang Normal University, School of Mathematics and Statistics (China)

- Publication Date:

- OSTI Identifier:
- 22769351

- 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; EQUATIONS; MATRICES; NONLINEAR PROBLEMS

### Citation Formats

```
Li, Cui-Xia, and Wu, Shi-Liang.
```*On LPMHSS-based iteration methods for a class of weakly nonlinear systems*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0395-8.

```
Li, Cui-Xia, & Wu, Shi-Liang.
```*On LPMHSS-based iteration methods for a class of weakly nonlinear systems*. United States. doi:10.1007/S40314-016-0395-8.

```
Li, Cui-Xia, and Wu, Shi-Liang. Tue .
"On LPMHSS-based iteration methods for a class of weakly nonlinear systems". United States. doi:10.1007/S40314-016-0395-8.
```

```
@article{osti_22769351,
```

title = {On LPMHSS-based iteration methods for a class of weakly nonlinear systems},

author = {Li, Cui-Xia and Wu, Shi-Liang},

abstractNote = {In this paper, for a class of the large sparse system of weakly nonlinear equations, combining separable property of the linear and nonlinear terms with the lopsided Hermitian and skew-Hermitian splitting (LHSS) of the coefficient matrix, the Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are presented. Theoretical analysis shows that these methods are locally convergent under suitable conditions. Numerical results show that both Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are feasible and effective for the large-scale system of weakly nonlinear equations.},

doi = {10.1007/S40314-016-0395-8},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}

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