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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Khosro Sayevand & Ahmad Pourdarvish & José A. Tenreiro Machado & Raziye Erfanifar, 2021. "On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus," Mathematics, MDPI, vol. 9(19), pages 1-23, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2501-:d:650679
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    References listed on IDEAS

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    1. Toutounian, F. & Buzhabadi, R., 2017. "New methods for computing the Drazin-inverse solution of singular linear systems," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 343-352.
    2. Pan, V.Y. & Soleymani, F. & Zhao, L., 2018. "An efficient computation of generalized inverse of a matrix," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 89-101.
    3. Mosić, Dijana & Djordjević, Dragan S., 2018. "Block representations of the generalized Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 200-209.
    4. Xiaoji Liu & Naping Cai, 2018. "High-Order Iterative Methods for the DMP Inverse," Journal of Mathematics, Hindawi, vol. 2018, pages 1-6, May.
    5. Wang, Xue-Zhong & Ma, Haifeng & Stanimirović, Predrag S., 2017. "Recurrent neural network for computing the W-weighted Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 300(C), pages 1-20.
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    Cited by:

    1. Yihui Lei & Zhengqi Dai & Bolin Liao & Guangping Xia & Yongjun He, 2022. "Double Features Zeroing Neural Network Model for Solving the Pseudoninverse of a Complex-Valued Time-Varying Matrix," Mathematics, MDPI, vol. 10(12), pages 1-19, June.

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