Fourth-Order Iterative Algorithms for the Simultaneous Calculation of Matrix Square Roots and Their Inverses
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| Publicado en: | Mathematics vol. 13, no. 21 (2025), p. 3370-3388 |
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| Acceso en línea: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 045 | 2 | |b d20250101 |b d20251231 | |
| 084 | |a 231533 |2 nlm | ||
| 100 | 1 | |a Zhu Jiameihui |u School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China | |
| 245 | 1 | |a Fourth-Order Iterative Algorithms for the Simultaneous Calculation of Matrix Square Roots and Their Inverses | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a This paper develops and analyzes new high-order iterative schemes for the effective evaluation of the matrix square root (MSR). By leveraging connections between the matrix sign function and the MSR, we design stable algorithms that exhibit fourth-order convergence under mild spectral conditions. Detailed error bounds and convergence analyses are provided, ensuring both theoretical rigor and numerical reliability. A comprehensive set of numerical experiments, conducted across structured and large-scale test matrices, demonstrates the superior performance of the proposed methods compared to classical approaches, both in terms of computational efficiency and accuracy. The results confirm that the proposed iterative strategies provide robust and scalable tools for practical applications requiring repeated computation of matrix square roots. | |
| 653 | |a Computational mathematics | ||
| 653 | |a Approximation | ||
| 653 | |a Iterative algorithms | ||
| 653 | |a Data science | ||
| 653 | |a Roots | ||
| 653 | |a Eigenvalues | ||
| 653 | |a Convergence | ||
| 653 | |a Algorithms | ||
| 653 | |a Iterative methods | ||
| 653 | |a Efficiency | ||
| 653 | |a Linear algebra | ||
| 700 | 1 | |a Li, Yutong |u School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China | |
| 700 | 1 | |a Li, Yilin |u School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China | |
| 700 | 1 | |a Liu, Tao |u School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China | |
| 700 | 1 | |a Ma, Qiang |u Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China | |
| 773 | 0 | |t Mathematics |g vol. 13, no. 21 (2025), p. 3370-3388 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3271047036/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3271047036/fulltextwithgraphics/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3271047036/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |