On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus
| Autor: | Raziye Erfanifar, Ahmad Pourdarvish, J.A.T. Machado, Khosro Sayevand |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Numerical linear algebra
non-smooth solution Iterative method General Mathematics Drazin inverse Caputo sense fractional calculus Moore–Penrose inverse Poisson distribution computer.software_genre Fractional calculus symbols.namesake Third order iterative method Computer Science (miscellaneous) symbols QA1-939 Applied mathematics convergence order Engineering (miscellaneous) computer Moore–Penrose pseudoinverse Mathematics |
| Zdroj: | Mathematics, Vol 9, Iss 2501, p 2501 (2021) Mathematics Volume 9 Issue 19 |
| ISSN: | 2227-7390 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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