A NEW FAMILY OF SECOND-ORDER ITERATIVE METHODS

FOR COMPUTING THE MOORE PENROSE INVERSE

BASED ON PENROSE EQUATIONS

FOR COMPUTING THE MOORE PENROSE INVERSE

BASED ON PENROSE EQUATIONS

Zainab Abu Iram^{1}, Ali Zein^{2}

^{1,2} Department of Applied Mathematics

Palestine Polytechnic University

Hebron, PALESTINE

Palestine Polytechnic University

Hebron, PALESTINE

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- [1] R. Burden, J. Faires, Numerical Analysis, 9th Ed. Brooks/Cole, Cengage Learning, Boston (2011).
- [2] H. Esmaeili, R. Erfanifar and M. Rashidi, A Fourth-order iterative method for computing the Moore-Penrose inverse, Journal of Hyperstructures, 6, No 1 (2017), 52-67.
- [3] R. Kress, Numerical Analysis, Springer-Verlag, New York (1998).
- [4] H. Li, T. Huang, Y. Zhang, X. Liu, and T. Gu, Chebyshev-type methods and preconditioning techniques, Applied Mathematics and Computation, 218 (2011), 260-270.
- [5] J. A. Marrero, R. Ben Taher, Y. El Khatabi, and M. Rachidi, On explicit formulas of the principal matrix pth root by polynomial decompositions, Applied Mathematics and Computation, 242 (2014), 435-443.
- [6] S. Miljkovic, M. Miladinovic, P. Stanimirovic, I. Stojanovic, Application of the pseudo-inverse computation in reconstruction of blurred images, Filomat, 26 (2012), 453-465.
- [7] M. Petkovic, and P. Stanimirovic, Iterative method for computing theMoore-Penrose inverse based on Penrose equations, Journal of Computational and Applied Mathematics, 235 (2011), 1604-1613.
- [8] R. Potthast and P. b. Graben, Inverse problems in neural field theory, SIAM Journal on Applied Dynamical Systems, 8 (2009), 1405-1433.
- [9] L. Sciavicco, B. Siciliano, Modelling and Control of Robot Manipulators, Springer-Verlag, London (2000).
- [10] G. Shultz, iterative Berechmmg der reziproken matrix, Z. Angew. Math. Mech., 13 (1933), 57-59.
- [11] F. Soleymani, M. Sharifi, and S. Shateyi, Approximating the inverse of a square matrix with application in computation of the Moore-Penrose Inverse, Journal of Applied Mathematics, 2014 (2014), 2-8.
- [12] S. Srivastava, D.K. Gupta, Higher order iterations for Moore-Penrose inverses, Journal of Applied Mathematics and Informatics, 32 (2014), 171-184.
- [13] P. Stanimirovic, D. Cvetkovic-Ilic, Successive matrix squaring algorithm for computing outer inverses, Applied Mathematics and Computation, 203 (2008), 19-29.
- [14] F. Toutounian, F. Soleymani, An iterative method for computing the approximate inverse of a square matrix and the Moore-Penrose inverse of a non-square matrix, Applied Mathematics and Computation, 224 (2013), 671-680.