Research Article

A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse

Volume: 3 Number: 2 June 30, 2020
Esmaeil Kokabifar *
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Communications in Advanced Mathematical Sciences Cover Communications in Advanced Mathematical Sciences
EN

A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse

Abstract

In this work, a family of iterative algorithms for approximating the inverse of a square matrix and the Moore-Penrose inverse of a non-square one is proposed. These methods are based on arbitrary high-order iterative techniques which are used for computing roots of a nonlinear function. Therefore the presented techniques occupy any high-order convergence. The proposed methods are convenient and self-explanatory, achieve satisfactory results, and also require less and easy computations compared to some current schemes. Experimental results are provided to illustrate the reliability and robustness of the techniques.

Keywords

Iterative method, Moore–Penrose, Approximate inverse

References

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  5. [5] G. Schulz, Iterative Berechnung der Reziproken matrix, Z. Angew. Math. Mech., 13 (1933), 57–59.
  6. [6] H. Saberi Najafi, M. Shams Solary, Computational algorithms for computing the inverse of a square matrix, quasi-inverse of a nonsquare matrix and block matrices, Appl. Math. Comput., 183 (2006), 539–550.
  7. [7] W. Li, Z. Li, A family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrix, Appl. Math. Comput., 215 (2010), 3433–3442.
  8. [8] H. Chen, Y. Wang, A family of higher-order convergent iterative methods for computing the Moore–Penrose inverse, Appl. Math. Comput., 218 (2011), 4012–4016.
  9. [9] C. Chun, Iterative methods improving Newton’s method by the decomposition method, Comput. Math. Appl., 50 (2005), 1559–1568.
  10. [10] J.F. Traub, Iterative Methods for Solution of Equations, Prentice-Hall, Englewood Cliffs, 1964.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Publication Date

June 30, 2020

Submission Date

April 11, 2020

Acceptance Date

June 24, 2020

Published in Issue

Year 2020 Volume: 3 Number: 2

DOI

https://doi.org/10.33434/cams.718365

IZ

https://izlik.org/JA35AL99UD

Cite

RIS / Bibtex
APA
Kokabifar, E. (2020). A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse. Communications in Advanced Mathematical Sciences, 3(2), 109-114. https://doi.org/10.33434/cams.718365
AMA
1.Kokabifar E. A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse. Communications in Advanced Mathematical Sciences. 2020;3(2):109-114. doi:10.33434/cams.718365
Chicago
Kokabifar, Esmaeil. 2020. “A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse”. Communications in Advanced Mathematical Sciences 3 (2): 109-14. https://doi.org/10.33434/cams.718365.
EndNote
Kokabifar E (June 1, 2020) A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse. Communications in Advanced Mathematical Sciences 3 2 109–114.
IEEE
[1]E. Kokabifar, “A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse”, Communications in Advanced Mathematical Sciences, vol. 3, no. 2, pp. 109–114, June 2020, doi: 10.33434/cams.718365.
ISNAD
Kokabifar, Esmaeil. “A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse”. Communications in Advanced Mathematical Sciences 3/2 (June 1, 2020): 109-114. https://doi.org/10.33434/cams.718365.
JAMA
1.Kokabifar E. A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse. Communications in Advanced Mathematical Sciences. 2020;3:109–114.
MLA
Kokabifar, Esmaeil. “A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse”. Communications in Advanced Mathematical Sciences, vol. 3, no. 2, June 2020, pp. 109-14, doi:10.33434/cams.718365.
Vancouver
1.Esmaeil Kokabifar. A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse. Communications in Advanced Mathematical Sciences. 2020 Jun. 1;3(2):109-14. doi:10.33434/cams.718365

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