# Factorizations of hyperpower family of iterative methods via least squares approach

## Abstract

A new method for finding proper factorizations of the hyperpower family of iterative methods for computing generalized inverses is proposed. The method is based on numerical optimization of an appropriate least squares problem. An iterative method in a non-normalized form for finding the generalized outer inverses with prescribed range and null space of any given complex matrix is proposed and considered. Computational complexity and convergence of the method are studied. Several numerical experiments are also presented.

- Authors:

- Panjab University Constituent College (India)
- University of Niš, Faculty of Sciences and Mathematics (Serbia)
- Institute for Advanced Studies in Basic Sciences, Department of Mathematics (Iran, Islamic Republic of)

- Publication Date:

- OSTI Identifier:
- 22769280

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 3; 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; COMPLEXES; CONVERGENCE; FACTORIZATION; ITERATIVE METHODS; LEAST SQUARE FIT; MATRICES; OPTIMIZATION

### Citation Formats

```
Kumar, Ashim, Stanimirović, Predrag S., Soleymani, Fazlollah, Krstić, Mihailo, and Rajković, Kostadin.
```*Factorizations of hyperpower family of iterative methods via least squares approach*. United States: N. p., 2018.
Web. doi:10.1007/S40314-017-0507-0.

```
Kumar, Ashim, Stanimirović, Predrag S., Soleymani, Fazlollah, Krstić, Mihailo, & Rajković, Kostadin.
```*Factorizations of hyperpower family of iterative methods via least squares approach*. United States. doi:10.1007/S40314-017-0507-0.

```
Kumar, Ashim, Stanimirović, Predrag S., Soleymani, Fazlollah, Krstić, Mihailo, and Rajković, Kostadin. Sun .
"Factorizations of hyperpower family of iterative methods via least squares approach". United States. doi:10.1007/S40314-017-0507-0.
```

```
@article{osti_22769280,
```

title = {Factorizations of hyperpower family of iterative methods via least squares approach},

author = {Kumar, Ashim and Stanimirović, Predrag S. and Soleymani, Fazlollah and Krstić, Mihailo and Rajković, Kostadin},

abstractNote = {A new method for finding proper factorizations of the hyperpower family of iterative methods for computing generalized inverses is proposed. The method is based on numerical optimization of an appropriate least squares problem. An iterative method in a non-normalized form for finding the generalized outer inverses with prescribed range and null space of any given complex matrix is proposed and considered. Computational complexity and convergence of the method are studied. Several numerical experiments are also presented.},

doi = {10.1007/S40314-017-0507-0},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 3,

volume = 37,

place = {United States},

year = {2018},

month = {7}

}

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