scholarly journals A note on the convergence of Halley's method for solving operator equations

1995 ◽  
Vol 37 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Shiming Zheng ◽  
Desmond Robbie
Keyword(s):  
Nonlinear Equations ◽  
Operator Equations ◽  
Halley’S Method ◽  
Halley's Method

AbstractHalley's method is a famous iteration for solving nonlinear equations. Some Kantorovich-like theorems have been given. The purpose of this note is to relax the region conditions and give another Kantorovich-like theorem for operator equations.

scholarly journals Convergence Theorem for a Family of New Modified Halley’s Method in Banach Space

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Rongfei Lin ◽  
Yueqing Zhao ◽  
Qingbiao Wu ◽  
Jueliang Hu
Keyword(s):  
Banach Space ◽  
Error Estimate ◽  
Convergence Theorem ◽  
Nonlinear Operator ◽  
Convergence Theorems ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Numerical Examples ◽  
Halley’S Method ◽  
Halley's Method

We establish convergence theorems of Newton-Kantorovich type for a family of new modified Halley’s method in Banach space to solve nonlinear operator equations. We present the corresponding error estimate. To show the application of our theorems, two numerical examples are given.

On the Geometry of Halley's Method

1995 ◽  
Vol 102 (5) ◽  
pp. 417-426 ◽  
Author(s):  
T. R. Scavo ◽  
J. B. Thoo
Keyword(s):  
Halley’S Method ◽  
Halley's Method

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

PAMM ◽  
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

Semilocal convergence for the Super-Halley’s method

2014 ◽  
Vol 7 (1) ◽  
pp. 70-84 ◽  
Author(s):  
M. Prashanth ◽  
D. K. Gupta ◽  
S. Singh
Keyword(s):  
Semilocal Convergence ◽  
Halley’S Method ◽  
Halley's Method
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