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

Esmaeil Kokabifar

doi:10.33434/cams.718365

Araştırma Makalesi

Yıl 2020, , 109 - 114, 30.06.2020

Esmaeil Kokabifar

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

Öz

Kaynakça

[1] A. Ben-Israel, T. N. E. Greville, Generalized Inverses, second ed., Springer, 2003.
[2] A. Ben-Israel, A. Charnes, Contributions to the theory of generalized inverses, SIAM J. App. Maths, 11 (3) (1963), 667–699.
[3] V. Pan and R. Sehreiber, An improved Newton iteration for the generalized inverse of a matrix, with applications, SIAM J. Sci. Statist. Comput. 12 (1991), 1109–1130.
[4] M. Z. Nashed, X. Chen, Convergence of Newton-like methods for singular operator equations using outer inverses, Numer. Math. 66 (1993), 235-257.
[5] G. Schulz, Iterative Berechnung der Reziproken matrix, Z. Angew. Math. Mech., 13 (1933), 57–59.
[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] 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] 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] C. Chun, Iterative methods improving Newton’s method by the decomposition method, Comput. Math. Appl., 50 (2005), 1559–1568.
[10] J.F. Traub, Iterative Methods for Solution of Equations, Prentice-Hall, Englewood Cliffs, 1964.
[11] M. A. Noor, K. I. Noor, M. Waseem, Higher-order iterative algorithms for solving nonlinear equations, World Appl. Sci. J., 16 (2012), 1657–1663.
[12] L. Grosz, Preconditioning by incomplete block elimination, Numer. Linear Algebra Appl., 7 (2000) 527–541.
[13] F. Soleymani, A Rapid Numerical Algorithm to Compute Matrix Inversion, Int. J. Maths. Math. Sci., (2012), Article ID 134653, 11 pages.

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

Yıl 2020, , 109 - 114, 30.06.2020

Esmaeil Kokabifar

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

Öz

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.

Anahtar Kelimeler

Iterative method, Moore–Penrose, Approximate inverse

Kaynakça

[1] A. Ben-Israel, T. N. E. Greville, Generalized Inverses, second ed., Springer, 2003.
[2] A. Ben-Israel, A. Charnes, Contributions to the theory of generalized inverses, SIAM J. App. Maths, 11 (3) (1963), 667–699.
[3] V. Pan and R. Sehreiber, An improved Newton iteration for the generalized inverse of a matrix, with applications, SIAM J. Sci. Statist. Comput. 12 (1991), 1109–1130.
[4] M. Z. Nashed, X. Chen, Convergence of Newton-like methods for singular operator equations using outer inverses, Numer. Math. 66 (1993), 235-257.
[5] G. Schulz, Iterative Berechnung der Reziproken matrix, Z. Angew. Math. Mech., 13 (1933), 57–59.
[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] 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] 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] C. Chun, Iterative methods improving Newton’s method by the decomposition method, Comput. Math. Appl., 50 (2005), 1559–1568.
[10] J.F. Traub, Iterative Methods for Solution of Equations, Prentice-Hall, Englewood Cliffs, 1964.
[11] M. A. Noor, K. I. Noor, M. Waseem, Higher-order iterative algorithms for solving nonlinear equations, World Appl. Sci. J., 16 (2012), 1657–1663.
[12] L. Grosz, Preconditioning by incomplete block elimination, Numer. Linear Algebra Appl., 7 (2000) 527–541.
[13] F. Soleymani, A Rapid Numerical Algorithm to Compute Matrix Inversion, Int. J. Maths. Math. Sci., (2012), Article ID 134653, 11 pages.

Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Makaleler
Yazarlar	Esmaeil Kokabifar
Yayımlanma Tarihi	30 Haziran 2020
Gönderilme Tarihi	11 Nisan 2020
Kabul Tarihi	24 Haziran 2020
Yayımlandığı Sayı	Yıl 2020

Kaynak Göster

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	Kokabifar E. A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse. Communications in Advanced Mathematical Sciences. Haziran 2020;3(2):109-114. doi:10.33434/cams.718365
Chicago	Kokabifar, Esmaeil. “A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse”. Communications in Advanced Mathematical Sciences 3, sy. 2 (Haziran 2020): 109-14. https://doi.org/10.33434/cams.718365.
EndNote	Kokabifar E (01 Haziran 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	E. Kokabifar, “A Family of Arbitrary High-Order Iterative Methods for Approximating Inverse and the Moore–Penrose Inverse”, Communications in Advanced Mathematical Sciences, c. 3, sy. 2, ss. 109–114, 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 (Haziran 2020), 109-114. https://doi.org/10.33434/cams.718365.
JAMA	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, c. 3, sy. 2, 2020, ss. 109-14, doi:10.33434/cams.718365.
Vancouver	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):109-14.