Unified Local Convergence for some High Order Methods with one Parameter
chebyshev-halley methods, banach space, local convergence
Abstract
The aim of this paper is to extend the applicability of some Chebyshev-Halley-type method with one parameter for solving nonlinear equations under weaker than before hypotheses on the second derivative.
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I Argyros (2007) Studies in Computational Mathematics 15. 15, ii.
I Argyros, D Chen, Q Quian (1994) The Jarratt method in Banach space setting. 51, 103-106.
I Argyros, Said Hilout (2013) Computational methods in nonlinear analysis.
A Behl, S Cordero, J Motsa, Torregrosa (2017) Stable high order iterative methods for solving nonlinear models. 303(15), 70-88.
V Candela, A Marquina (1990) Recurrence relations for rational cubic methods I: The Halley method. 44(2), 169-184.
V Candela, A Marquina (1990) Recurrence relations for rational cubic methods II: The Chebyshev method. 45(4), 355-367.
J Ezquerro, M Hernández (1999) On a class of iterations containing the Chebyshev and the Halley methods. 54(3-4), 403-415.
J Ezquero, M Hernandez (2003) A new class of third order methods in Banach spaces. 31, 181-199.
M Hernandez, J Gutiérrez (1997) Third order iterative methods for operators with bounded second derivative. 82, 171-183.
M Hernández, M Salanova (1999) Sufficient conditions for semilocal convergence of a fourth order multipoint iterative method for solving equations in Banach spaces. 1, 29-40.
P Jarratt (1996) Some fourth order multipoint iterative methods for solving equations. 20(95), 434-437.
P Parida, D Gupta (2007) Recurrence relations for a Newton-like method in Banach spaces. 206(2), 873-887.
M Prashanth, D Gupta (2013) A CONTINUATION METHOD AND ITS CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS IN BANACH SPACES. 10(04), 1350021.
W Rheinboldt (1977) An adaptive continuation process for solving systems of nonlinear equations. 129-142.
J Traub (1982) Iterative methods for the solution of equations.
X Wang, J Kou, C Gu (2011) Semilocal convergence of a sixth-order Jarratt method in Banach spaces. 57, 441-456.
X Wang, J Kou R-order of convergence for modified Jarratt method with less computation of inversion.
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2017-12-19
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