A Sixth-Order Iterative Scheme Through Weighted Rational Approximations for Computing the Matrix Sign Function
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| Опубліковано в:: | Mathematics vol. 13, no. 17 (2025), p. 2849-2864 |
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| Автор: | |
| Інші автори: | , , , |
| Опубліковано: |
MDPI AG
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| Предмети: | |
| Онлайн доступ: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 045 | 2 | |b d20250101 |b d20251231 | |
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| 100 | 1 | |a Zhang, Ce |u Modern Educational Technology Center, Changchun Guanghua University, Changchun 130033, China; zhangce@ghu.edu.cn | |
| 245 | 1 | |a A Sixth-Order Iterative Scheme Through Weighted Rational Approximations for Computing the Matrix Sign Function | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a This work introduces a sixth-order multi-step iterative algorithm for obtaining the matrix sign function of nonsingular matrices. The presented methodology employs optimized rational approximations combined with strategically formulated weight functions to achieve both computational efficiency and numerical precision. We present a convergence study that includes the analytical derivation of error terms, formally proving the sixth-order convergence characteristics. Numerical simulations substantiate the theoretical results and demonstrate the algorithm’s advantage over current state-of-the-art approaches in terms of both accuracy and computational performance. | |
| 653 | |a Control theory | ||
| 653 | |a Approximation | ||
| 653 | |a Iterative algorithms | ||
| 653 | |a Methods | ||
| 653 | |a Eigenvalues | ||
| 653 | |a Convergence | ||
| 653 | |a Algorithms | ||
| 653 | |a Weighting functions | ||
| 653 | |a Iterative methods | ||
| 653 | |a Linear algebra | ||
| 700 | 1 | |a Zhao, Bo |u School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China; 202215092@stu.neuq.edu.cn (B.Z.); 2472156@stu.neu.edu.cn (W.R.); 2401995@stu.neu.edu.cn (R.C.) | |
| 700 | 1 | |a Ren Wenjing |u School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China; 202215092@stu.neuq.edu.cn (B.Z.); 2472156@stu.neu.edu.cn (W.R.); 2401995@stu.neu.edu.cn (R.C.) | |
| 700 | 1 | |a Cao Ruosong |u School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China; 202215092@stu.neuq.edu.cn (B.Z.); 2472156@stu.neu.edu.cn (W.R.); 2401995@stu.neu.edu.cn (R.C.) | |
| 700 | 1 | |a Liu, Tao |u School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China; 202215092@stu.neuq.edu.cn (B.Z.); 2472156@stu.neu.edu.cn (W.R.); 2401995@stu.neu.edu.cn (R.C.) | |
| 773 | 0 | |t Mathematics |g vol. 13, no. 17 (2025), p. 2849-2864 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3249692154/abstract/embedded/75I98GEZK8WCJMPQ?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3249692154/fulltextwithgraphics/embedded/75I98GEZK8WCJMPQ?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3249692154/fulltextPDF/embedded/75I98GEZK8WCJMPQ?source=fedsrch |