Julia sets for the super-Newton method, Cauchy’s method, and Halley’s method

Kyle Kneisl

doi:10.1063/1.1368137

Julia sets for the super-Newton method, Cauchy’s method, and Halley’s method

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.1368137 ◽

2001 ◽

Vol 11 (2) ◽

pp. 359-370 ◽

Cited By ~ 43

Author(s):

Kyle Kneisl

Keyword(s):

Newton Method ◽

Julia Sets ◽

Halley’S Method ◽

Halley's Method ◽

Cauchy's Method

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Julia sets for the standard Newton’s method, Halley’s method, and Schröder’s method

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.12.002 ◽

2007 ◽

Vol 189 (2) ◽

pp. 1186-1195 ◽

Cited By ~ 9

Author(s):

Xingyuan Wang ◽

Xuejing Yu

Keyword(s):

Newton’S Method ◽

Newton's Method ◽

Julia Sets ◽

Halley’S Method ◽

Schröder’S Method ◽

Halley's Method

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Some variants of Halley’s method with memory and their applications for solving several chemical problems

Journal of Mathematical Chemistry ◽

10.1007/s10910-020-01108-3 ◽

2020 ◽

Vol 58 (4) ◽

pp. 751-774 ◽

Cited By ~ 1

Author(s):

Alicia Cordero ◽

Higinio Ramos ◽

Juan R. Torregrosa

Keyword(s):

Halley’S Method ◽

Halley's Method ◽

With Memory

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On the Geometry of Halley's Method

American Mathematical Monthly ◽

10.1080/00029890.1995.12004594 ◽

1995 ◽

Vol 102 (5) ◽

pp. 417-426 ◽

Cited By ~ 10

Author(s):

T. R. Scavo ◽

J. B. Thoo

Keyword(s):

Halley’S Method ◽

Halley's Method

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A generalization of the Kantorovich type assumptions for Halley's method

International Journal of Computer Mathematics ◽

10.1080/00207160701331335 ◽

2007 ◽

Vol 84 (12) ◽

pp. 1771-1779 ◽

Cited By ~ 2

Author(s):

J. A. Ezquerro ◽

M. A. Hernández

Keyword(s):

Halley’S Method ◽

Halley's Method ◽

Kantorovich Type Assumptions

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Use of Halley's Method in the Nonlinear Finite Element Analysis

PAMM ◽

10.1002/pamm.201010277 ◽

2010 ◽

Vol 10 (1) ◽

pp. 569-570

Author(s):

Carolin Plate ◽

Panayiotis Papadopoulos ◽

Ralf Müller

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Nonlinear Finite Element Analysis ◽

Nonlinear Finite Element ◽

Element Analysis ◽

Halley’S Method ◽

Halley's Method

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Convergence radius of Halley’s method for multiple roots under center-Hölder continuous condition

Applied Mathematics and Computation ◽

10.1016/j.amc.2015.05.147 ◽

2015 ◽

Vol 265 ◽

pp. 1011-1018

Author(s):

Suzhen Liu ◽

Yongzhong Song ◽

Xiaojian Zhou

Keyword(s):

Multiple Roots ◽

Convergence Radius ◽

Hölder Continuous ◽

Halley’S Method ◽

Halley's Method

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Semilocal convergence for the Super-Halley’s method

Numerical Analysis and Applications ◽

10.1134/s1995423914010078 ◽

2014 ◽

Vol 7 (1) ◽

pp. 70-84 ◽

Cited By ~ 3

Author(s):

M. Prashanth ◽

D. K. Gupta ◽

S. Singh

Keyword(s):

Semilocal Convergence ◽

Halley’S Method ◽

Halley's Method

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Newton–Kantorovich theorem for a family of modified Halley’s method under Hölder continuity conditions in Banach space

Applied Mathematics and Computation ◽

10.1016/j.amc.2008.02.004 ◽

2008 ◽

Vol 202 (1) ◽

pp. 243-251 ◽

Cited By ~ 12

Author(s):

Yueqing Zhao ◽

Qingbiao Wu

Keyword(s):

Banach Space ◽

Hölder Continuity ◽

Holder Continuity ◽

Kantorovich Theorem ◽

Halley’S Method ◽

Halley's Method

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A note on Halley's method

Computers & Graphics ◽

10.1016/0097-8493(91)90034-f ◽

1991 ◽

Vol 15 (1) ◽

pp. 89-90 ◽

Cited By ~ 5

Author(s):

Ray Reeves

Keyword(s):

Halley’S Method ◽

Halley's Method

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Halley's method for operators with unbounded second derivative

Applied Numerical Mathematics ◽

10.1016/j.apnum.2006.05.001 ◽

2007 ◽

Vol 57 (3) ◽

pp. 354-360 ◽

Cited By ~ 19

Author(s):

J.A. Ezquerro ◽

M.A. Hernández

Keyword(s):

Second Derivative ◽

Halley’S Method ◽

Halley's Method

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