On the Construction of a Two-Step Sixth-Order Scheme to Find the Drazin Generalized Inverse
This study introduces a numerically efficient iterative solver for computing the Drazin generalized inverse, addressing a critical need for high-performance methods in matrix computations. The proposed two-step scheme achieves sixth-order convergence, distinguishing it as a higher-order method that...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/14/1/22 |
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| _version_ | 1832589133192626176 |
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| author | Keyang Zhang Fazlollah Soleymani Stanford Shateyi |
| author_facet | Keyang Zhang Fazlollah Soleymani Stanford Shateyi |
| author_sort | Keyang Zhang |
| collection | DOAJ |
| description | This study introduces a numerically efficient iterative solver for computing the Drazin generalized inverse, addressing a critical need for high-performance methods in matrix computations. The proposed two-step scheme achieves sixth-order convergence, distinguishing it as a higher-order method that outperforms several existing approaches. A rigorous convergence analysis is provided, highlighting the importance of selecting an appropriate initial value to ensure robustness. Extensive numerical experiments validate the analytical findings, showcasing the method’s superior speed and efficiency, making it an advancement in iterative solvers for generalized inverses. |
| format | Article |
| id | doaj-art-99928b8a7c474dae85dfbd2a85526933 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-99928b8a7c474dae85dfbd2a855269332025-01-24T13:22:10ZengMDPI AGAxioms2075-16802024-12-011412210.3390/axioms14010022On the Construction of a Two-Step Sixth-Order Scheme to Find the Drazin Generalized InverseKeyang Zhang0Fazlollah Soleymani1Stanford Shateyi2Department of Mathematical Sciences, New Jersey Institute of Technology, 323 Martin Luther King Blvd., Newark, NJ 07102, USADepartment of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, IranDepartment of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South AfricaThis study introduces a numerically efficient iterative solver for computing the Drazin generalized inverse, addressing a critical need for high-performance methods in matrix computations. The proposed two-step scheme achieves sixth-order convergence, distinguishing it as a higher-order method that outperforms several existing approaches. A rigorous convergence analysis is provided, highlighting the importance of selecting an appropriate initial value to ensure robustness. Extensive numerical experiments validate the analytical findings, showcasing the method’s superior speed and efficiency, making it an advancement in iterative solvers for generalized inverses.https://www.mdpi.com/2075-1680/14/1/22generalized inverseorder of convergencenumerical methodinitial matrixDrazin |
| spellingShingle | Keyang Zhang Fazlollah Soleymani Stanford Shateyi On the Construction of a Two-Step Sixth-Order Scheme to Find the Drazin Generalized Inverse Axioms generalized inverse order of convergence numerical method initial matrix Drazin |
| title | On the Construction of a Two-Step Sixth-Order Scheme to Find the Drazin Generalized Inverse |
| title_full | On the Construction of a Two-Step Sixth-Order Scheme to Find the Drazin Generalized Inverse |
| title_fullStr | On the Construction of a Two-Step Sixth-Order Scheme to Find the Drazin Generalized Inverse |
| title_full_unstemmed | On the Construction of a Two-Step Sixth-Order Scheme to Find the Drazin Generalized Inverse |
| title_short | On the Construction of a Two-Step Sixth-Order Scheme to Find the Drazin Generalized Inverse |
| title_sort | on the construction of a two step sixth order scheme to find the drazin generalized inverse |
| topic | generalized inverse order of convergence numerical method initial matrix Drazin |
| url | https://www.mdpi.com/2075-1680/14/1/22 |
| work_keys_str_mv | AT keyangzhang ontheconstructionofatwostepsixthorderschemetofindthedrazingeneralizedinverse AT fazlollahsoleymani ontheconstructionofatwostepsixthorderschemetofindthedrazingeneralizedinverse AT stanfordshateyi ontheconstructionofatwostepsixthorderschemetofindthedrazingeneralizedinverse |