Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions
Abstract
:1. Introduction
2. Semilocal Analysis
- linear operator , where and , is invertible;
- Equations (3) and (4) hold on D, Equations (6) and (7) hold on ;
- equation
- , , .
- exists and ;
- ;
- .
- linear operator , where and , is invertible;
- Equations (8)–(11) hold;
- numbers , γ and such that
- linear operator , where and , is invertible;
- numbers and such that Equation (12) is satisfied;
- the Lipschitz conditions are fulfilled for eachand for each
- equation
- , , .
3. Numerical Results
Author Contributions
Funding
Conflicts of Interest
References
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n | |||||
---|---|---|---|---|---|
1 | 2.0602 × 10 | 6.8518 × 10 | 9.7951 × 10 | 9.1409 × 10 | 1.5738× 10 |
2 | 3.1428 × 10 | 8.9551 × 10 | 4.2097 × 10 | 1.1958 × 10 | 6.7636 × 10 |
3 | 7.0617 × 10 | 5.2824 × 10 | 6.4218 × 10 | 7.0457 × 10 | 1.0318 × 10 |
4 | 0 | 1.8032 × 10 | 1.4429 × 10 | 2.4050 × 10 | 2.3184 × 10 |
n | |||||
---|---|---|---|---|---|
1 | 7.3779 × 10 | 3.1227 × 10 | 2.3990 × 10 | 4.2444 × 10 | 2.1541 × 10 |
2 | 3.9991 × 10 | 1.6564 × 10 | 6.0489 × 10 | 2.2443 × 10 | 5.4314 × 10 |
3 | 1.1419 × 10 | 2.1230 × 10 | 3.2787 × 10 | 2.8737 × 10 | 2.9440 × 10 |
4 | 0 | 3.2808 × 10 | 9.3616 × 10 | 4.4410 × 10 | 8.4060 × 10 |
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Argyros, I.K.; Shakhno, S.; Yarmola, H. Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions. Computation 2020, 8, 8. https://doi.org/10.3390/computation8010008
Argyros IK, Shakhno S, Yarmola H. Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions. Computation. 2020; 8(1):8. https://doi.org/10.3390/computation8010008
Chicago/Turabian StyleArgyros, Ioannis K., Stepan Shakhno, and Halyna Yarmola. 2020. "Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions" Computation 8, no. 1: 8. https://doi.org/10.3390/computation8010008
APA StyleArgyros, I. K., Shakhno, S., & Yarmola, H. (2020). Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions. Computation, 8(1), 8. https://doi.org/10.3390/computation8010008