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Newton Method
Nonlinear Equation
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A modification of Newton's method for nondifferentiable equations
A modification of Newton's method for nondifferentiable equations,10.1016/S03770427(03)006502,Journal of Computational and Applied Mathematics,M. A
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A modification of Newton's method for nondifferentiable equations
(
Citations: 4
)
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M. A Hernández
,
M. J Rubio
In this paper, we study the problem of approximating a solution of a
nonlinear equation
where the operator involved is nondifferentiable. Having the
Newton method
as origin we construct a uniparametric family of iterative processes to approximate a solution of the equation. To finish we consider several test problems.
Journal:
Journal of Computational and Applied Mathematics  J COMPUT APPL MATH
, vol. 164, pp. 409417, 2004
DOI:
10.1016/S03770427(03)006502
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Citation Context
(1)
...A semilocal convergence analysis for Secant method was presented in [15,
16
] using assumption (5) in the particular case F ≡ 0i n (4)...
Ioannis K. Argyros
,
et al.
An improved local convergence analysis for Newton–Steffensentype meth...
References
(10)
A convergence theorem for Newtonlike methods under generalized ChenYamamototype assumptions
(
Citations: 11
)
I Argyros
Journal:
Applied Mathematics and Computation  AMC
, vol. 61, no. 1, pp. 2537, 1994
The Newton Method for Operators with Hölder Continuous First Derivative
(
Citations: 21
)
M. A. Hernández
Journal:
Journal of Optimization Theory and Applications  J OPTIMIZ THEOR APPL
, vol. 109, no. 3, pp. 631648, 2001
A new type of recurrence relations for the secant method
(
Citations: 4
)
M. A. Hernández
,
M. J. Rubio
Journal:
International Journal of Computer Mathematics  IJCM
, vol. 72, no. 4, pp. 477490, 1999
Semilocal convergence of the secant method under mild convergence conditions of differentiability
(
Citations: 27
)
M. A. Hernández
,
M. J. Rubio
Journal:
Computers & Mathematics With Applications  COMPUT MATH APPL
, vol. 44, no. 3, pp. 277285, 2002
The Secant method for nondifferentiable operators
(
Citations: 12
)
Miguel A. Hernández
,
M. Jóse Rubio
Journal:
Applied Mathematics Letters
, vol. 15, no. 4, pp. 395399, 2002
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Citations
(4)
An improved local convergence analysis for Newton–Steffensentype method
Ioannis K. Argyros
,
Saïd Hilout
Journal:
Journal of Applied Mathematics and Computing
, vol. 32, no. 1, pp. 111118, 2010
Convergence analysis of a family of Steffensentype methods for generalized equations
(
Citations: 6
)
Saïd Hilout
Journal:
Journal of Mathematical Analysis and Applications  J MATH ANAL APPL
, vol. 339, no. 2, pp. 753761, 2008
A noniterative derivativefree method for nonlinear ordinary differential equations
(
Citations: 2
)
J. I. Ramos
Journal:
Applied Mathematics and Computation  AMC
, vol. 203, no. 2, pp. 672678, 2008
Reference variable methods of solving minmax optimization problems
(
Citations: 1
)
Baiquan Lu
,
Yuan Cao
,
Min Jie Yuan
,
Jianzhen Zhou
Journal:
Journal of Global Optimization
, vol. 42, no. 1, pp. 121, 2008