Fractal basins of attraction associated with a damped Newton's method
Publication
, Journal Article
Epureanu, BI; Greenside, HS
Published in: SIAM Review
January 1, 1998
An intriguing and unexpected result for students learning numerical analysis is that Newton's method, applied to the simple polynomial z3 - 1 = 0 in the complex plane, leads to intricately interwoven basins of attraction of the roots. As an example of an interesting open question that may help to stimulate student interest in numerical analysis, we investigate the question of whether a damping method, which is designed to increase the likelihood of convergence for Newton's method, modifies the fractal structure of the basin boundaries. The overlap of the frontiers of numerical analysis and nonlinear dynamics provides many other problems that can help to make numerical analysis courses interesting.
Duke Scholars
Published In
SIAM Review
DOI
ISSN
0036-1445
Publication Date
January 1, 1998
Volume
40
Issue
1
Start / End Page
102 / 109
Related Subject Headings
- Numerical & Computational Mathematics
- 4901 Applied mathematics
- 0906 Electrical and Electronic Engineering
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Epureanu, B. I., & Greenside, H. S. (1998). Fractal basins of attraction associated with a damped Newton's method. SIAM Review, 40(1), 102–109. https://doi.org/10.1137/S0036144596310033
Epureanu, B. I., and H. S. Greenside. “Fractal basins of attraction associated with a damped Newton's method.” SIAM Review 40, no. 1 (January 1, 1998): 102–9. https://doi.org/10.1137/S0036144596310033.
Epureanu BI, Greenside HS. Fractal basins of attraction associated with a damped Newton's method. SIAM Review. 1998 Jan 1;40(1):102–9.
Epureanu, B. I., and H. S. Greenside. “Fractal basins of attraction associated with a damped Newton's method.” SIAM Review, vol. 40, no. 1, Jan. 1998, pp. 102–09. Scopus, doi:10.1137/S0036144596310033.
Epureanu BI, Greenside HS. Fractal basins of attraction associated with a damped Newton's method. SIAM Review. 1998 Jan 1;40(1):102–109.
Published In
SIAM Review
DOI
ISSN
0036-1445
Publication Date
January 1, 1998
Volume
40
Issue
1
Start / End Page
102 / 109
Related Subject Headings
- Numerical & Computational Mathematics
- 4901 Applied mathematics
- 0906 Electrical and Electronic Engineering
- 0102 Applied Mathematics