메뉴 건너뛰기




Volumn 215, Issue 3, 2009, Pages 1084-1090

Newton's method's basins of attraction revisited

Author keywords

Iteration methods; Newton Raphson methods; Nodules

Indexed keywords

BASINS OF ATTRACTION; ITERATION METHODS; MODIFIED NEWTON METHOD; NEWTON'S METHODS; NODULES; NUMBER OF ITERATIONS; SIMPLE ALGORITHM;

EID: 69249220033     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.06.041     Document Type: Article
Times cited : (43)

References (33)
  • 2
    • 49449118465 scopus 로고
    • Historical note on the Newton-Raphson method of approximation
    • Cajori F. Historical note on the Newton-Raphson method of approximation. Am. Math. Monthly 18 2 (1911) 19-33
    • (1911) Am. Math. Monthly , vol.18 , Issue.2 , pp. 19-33
    • Cajori, F.1
  • 3
    • 0029535607 scopus 로고
    • Historical development of the Newton-Raphson method
    • Ypma T.J. Historical development of the Newton-Raphson method. SIAM Rev. 37 4 (1995) 531-551
    • (1995) SIAM Rev. , vol.37 , Issue.4 , pp. 531-551
    • Ypma, T.J.1
  • 4
    • 34447609127 scopus 로고
    • Über unendlich viele Algorithmen zur Auflösung der Gleichungen
    • English translation by G.W. Stewart, On infinitely many algorithms for solving equations, Technical Report TR-92-121, Department of Computer Science, University of Maryland, College Park, MD, USA, 1992
    • Schröder E. Über unendlich viele Algorithmen zur Auflösung der Gleichungen. Math. Annal. 2 (1870) 317-365 English translation by G.W. Stewart, On infinitely many algorithms for solving equations, Technical Report TR-92-121, Department of Computer Science, University of Maryland, College Park, MD, USA, 1992
    • (1870) Math. Annal. , vol.2 , pp. 317-365
    • Schröder, E.1
  • 7
    • 0034546528 scopus 로고    scopus 로고
    • Historical developments in convergence analysis for Newton's and Newton-like methods
    • Yamamoto T. Historical developments in convergence analysis for Newton's and Newton-like methods. J. Comput. Appl. Math. 124 (2000) 1-23
    • (2000) J. Comput. Appl. Math. , vol.124 , pp. 1-23
    • Yamamoto, T.1
  • 8
    • 0042522428 scopus 로고    scopus 로고
    • Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method
    • Abbasbandy S. Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method. Appl. Math. Comput. 145 (2003) 887-893
    • (2003) Appl. Math. Comput. , vol.145 , pp. 887-893
    • Abbasbandy, S.1
  • 10
    • 3943092529 scopus 로고    scopus 로고
    • Comparison of homotopy perturbation method and homotopy analysis method
    • He J.-H. Comparison of homotopy perturbation method and homotopy analysis method. Appl. Math. Comput. 156 (2004) 527-539
    • (2004) Appl. Math. Comput. , vol.156 , pp. 527-539
    • He, J.-H.1
  • 11
    • 25844456083 scopus 로고    scopus 로고
    • Comparison between the homotopy analysis method and homotopy perturbation method
    • Liao S.-J. Comparison between the homotopy analysis method and homotopy perturbation method. Appl. Math. Comput. 169 (2005) 1186-1194
    • (2005) Appl. Math. Comput. , vol.169 , pp. 1186-1194
    • Liao, S.-J.1
  • 12
    • 26044450586 scopus 로고    scopus 로고
    • A study of convergence on the Newton-homotopy continuation method
    • Wu T.-M. A study of convergence on the Newton-homotopy continuation method. Appl. Math. Comput. 168 (2005) 1169-1174
    • (2005) Appl. Math. Comput. , vol.168 , pp. 1169-1174
    • Wu, T.-M.1
  • 13
    • 0032635295 scopus 로고    scopus 로고
    • On rediscovered iteration methods for solving equations
    • Petković M.S., and Herceg D. On rediscovered iteration methods for solving equations. J. Comput. Appl. Math. 107 (1999) 275-284
    • (1999) J. Comput. Appl. Math. , vol.107 , pp. 275-284
    • Petković, M.S.1    Herceg, D.2
  • 14
    • 33847003021 scopus 로고    scopus 로고
    • A note on some recent methods for solving nonlinear equations
    • Petković L.D., and Petković M.S. A note on some recent methods for solving nonlinear equations. Appl. Math. Comput. 185 (2007) 368-374
    • (2007) Appl. Math. Comput. , vol.185 , pp. 368-374
    • Petković, L.D.1    Petković, M.S.2
  • 15
    • 69249245388 scopus 로고    scopus 로고
    • P. Sebah, X. Gourdon, Newton's method and high order iterations, Technical Report, 2001 (unpublished); Available at: .
    • P. Sebah, X. Gourdon, Newton's method and high order iterations, Technical Report, 2001 (unpublished); Available at: .
  • 16
    • 33846609124 scopus 로고    scopus 로고
    • Generation of root finding algorithms via perturbation theory and some formulas
    • Pakdemirli M., and Boyaci{dotless} H. Generation of root finding algorithms via perturbation theory and some formulas. Appl. Math. Comput. 184 (2007) 783-788
    • (2007) Appl. Math. Comput. , vol.184 , pp. 783-788
    • Pakdemirli, M.1    Boyaci, H.2
  • 18
    • 0035647444 scopus 로고    scopus 로고
    • How to find all roots of complex polynomials by Newton's method
    • Hubbard J.H., Schleicher D., and Sutherland S. How to find all roots of complex polynomials by Newton's method. Invent. Math. 146 1 (2001) 1-33
    • (2001) Invent. Math. , vol.146 , Issue.1 , pp. 1-33
    • Hubbard, J.H.1    Schleicher, D.2    Sutherland, S.3
  • 19
    • 69249236893 scopus 로고    scopus 로고
    • Review of some iterative root-finding methods from a dynamical point of view
    • Amat S., Busquier S., and Plaza S. Review of some iterative root-finding methods from a dynamical point of view. Sci. Ser. A: Math. Sci. 10 (2004) 3-35
    • (2004) Sci. Ser. A: Math. Sci. , vol.10 , pp. 3-35
    • Amat, S.1    Busquier, S.2    Plaza, S.3
  • 20
    • 0036003374 scopus 로고    scopus 로고
    • Graphic and numerical comparison between iterative methods
    • Varona J.L. Graphic and numerical comparison between iterative methods. Math. Intell. 24 1 (2002) 37-46
    • (2002) Math. Intell. , vol.24 , Issue.1 , pp. 37-46
    • Varona, J.L.1
  • 21
    • 69249241779 scopus 로고    scopus 로고
    • Approximations of continuous Newton's method: an extension of Cayley's problem
    • Jacobsen J., Lewis O., and Tennis B. Approximations of continuous Newton's method: an extension of Cayley's problem. Electron. J. Diff. Equat. 15 (2007) 163-173
    • (2007) Electron. J. Diff. Equat. , vol.15 , pp. 163-173
    • Jacobsen, J.1    Lewis, O.2    Tennis, B.3
  • 23
    • 0026358285 scopus 로고
    • Computer art from numerical methods
    • Szyszkowicz M. Computer art from numerical methods. Comput. Graph. Forum 10 3 (1991) 255-259
    • (1991) Comput. Graph. Forum , vol.10 , Issue.3 , pp. 255-259
    • Szyszkowicz, M.1
  • 24
    • 45549120987 scopus 로고
    • Overrelaxation and chaos
    • Pickover C.A. Overrelaxation and chaos. Phys. Lett. A 130 3 (1988) 125-128
    • (1988) Phys. Lett. A , vol.130 , Issue.3 , pp. 125-128
    • Pickover, C.A.1
  • 26
    • 69249247000 scopus 로고    scopus 로고
    • Basin of attraction
    • Ott E. Basin of attraction. Scholarpedia 1 8 (2006) 1701
    • (2006) Scholarpedia , vol.1 , Issue.8 , pp. 1701
    • Ott, E.1
  • 27
    • 0025757579 scopus 로고
    • A note on Halley's method
    • Reeves R. A note on Halley's method. Comput. Graph. 15 1 (1991) 89-90
    • (1991) Comput. Graph. , vol.15 , Issue.1 , pp. 89-90
    • Reeves, R.1
  • 28
    • 0026880846 scopus 로고
    • Further insights into Halley's method
    • Reeves R. Further insights into Halley's method. Comput. Graph. 16 (1992) 235-236
    • (1992) Comput. Graph. , vol.16 , pp. 235-236
    • Reeves, R.1
  • 29
    • 33846645408 scopus 로고    scopus 로고
    • Comments on the Basto-Semiao-Calheiros root finding method
    • Petković M.S. Comments on the Basto-Semiao-Calheiros root finding method. Appl. Math. Comput. 184 (2007) 143-148
    • (2007) Appl. Math. Comput. , vol.184 , pp. 143-148
    • Petković, M.S.1
  • 30
    • 2542502724 scopus 로고    scopus 로고
    • Polynomiography and applications in art, education and science
    • Kalantari B. Polynomiography and applications in art, education and science. Comput. Graph. 28 (2004) 417-430
    • (2004) Comput. Graph. , vol.28 , pp. 417-430
    • Kalantari, B.1
  • 31
    • 34249819938 scopus 로고    scopus 로고
    • On general convergence in extracting radicals via a fundamental family of iteration functions
    • Jin Y., and Kalantari B. On general convergence in extracting radicals via a fundamental family of iteration functions. J. Comput. Appl. Math. 206 (2007) 832-842
    • (2007) J. Comput. Appl. Math. , vol.206 , pp. 832-842
    • Jin, Y.1    Kalantari, B.2
  • 32
    • 69249238031 scopus 로고    scopus 로고
    • B. Kalantari, On homogeneous linear recurrence relations and approximation of zeros of complex polynomials, in: M.B. Nathanson (Ed.), Unusual Applications of Number Theory, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 64, 2000, pp. 125-144.
    • B. Kalantari, On homogeneous linear recurrence relations and approximation of zeros of complex polynomials, in: M.B. Nathanson (Ed.), Unusual Applications of Number Theory, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 64, 2000, pp. 125-144.
  • 33
    • 0028445851 scopus 로고
    • Accelerated convergence in Newton's method
    • Gerlach J. Accelerated convergence in Newton's method. SIAM Rev. 36 (1994) 272-276
    • (1994) SIAM Rev. , vol.36 , pp. 272-276
    • Gerlach, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.