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Ahmad Pourdarvish

Ahmad Pourdarvish

Academic rank: Professor
ORCID:
Education: PhD.
ScopusId:
HIndex:
Faculty: Faculty of Mathematical Sciences
Address:
Phone: 01135302470

Research

Title
On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus
Type
JournalPaper
Keywords
Caputo sense; convergence order; Drazin inverse; fractional calculus; iterative method; Moore–Penrose inverse; non-smooth solution
Year
2021
Journal Mathematics
DOI
Researchers Khosro Sayevand ، Ahmad Pourdarvish ، Jose Antonio Tenreiro Machado

Abstract

This paper presents a third order iterative method for obtaining the Moore–Penrose and Drazin inverses with a computational cost of O(n3), 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. View Full-Text