On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus

Khosro Sayevand, Ahmad Pourdarvish, José A. Tenreiro Machado and Raziye Erfanifar
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Khosro Sayevand: Faculty of Mathematical Sciences, Malayer University, Malayer P.O. Box 16846-13114, Iran
Ahmad Pourdarvish: Faculty of Mathematical Sciences, Department of Statistics, Mazandaran University, Mazandaran P.O. Box 47416-135534, Iran
José A. Tenreiro Machado: Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, 4249-015 Porto, Portugal
Raziye Erfanifar: Faculty of Mathematical Sciences, Malayer University, Malayer P.O. Box 16846-13114, Iran

Mathematics, 2021, vol. 9, issue 19, 1-23

Abstract: This paper presents a third order iterative method for obtaining the Moore–Penrose and Drazin inverses with a computational cost of O ( n 3 ) , where n ? N . The performance of the new approach is compared with other methods discussed in the literature. The results show that the algorithm is remarkably efficient and accurate. Furthermore, sufficient criteria in the fractional sense are presented, both for smooth and non-smooth solutions. The fractional elliptic Poisson and fractional sub-diffusion equations in the Caputo sense are considered as prototype examples. The results can be extended to other scientific areas involving numerical linear algebra.

Keywords: Caputo sense; convergence order; Drazin inverse; fractional calculus; iterative method; Moore–Penrose inverse; non-smooth solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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