On a class of iterative procedures for solving nonlinear equations in Banach spaces
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Displaying 1 – 20 of 41
On a new method for enlarging the radius of convergence for Newton's method
Ioannis K. Argyros (2001)
Applicationes Mathematicae
We provide new local and semilocal convergence results for Newton's method. We introduce Lipschitz-type hypotheses on the mth-Frechet derivative. This way we manage to enlarge the radius of convergence of Newton's method. Numerical examples are also provided to show that our results guarantee convergence where others do not.
On a quadratically convergent method using divided differences of order one under the gamma condition
Ioannis Argyros, Hongmin Ren (2008)
Open Mathematics
We re-examine a quadratically convergent method using divided differences of order one in order to approximate a locally unique solution of an equation in a Banach space setting [4, 5, 7]. Recently in [4, 5, 7], using Lipschitz conditions, and a Newton-Kantorovich type approach, we provided a local as well as a semilocal convergence analysis for this method which compares favorably to other methods using two function evaluations such as the Steffensen’s method [1, 3, 13]. Here, we provide an analysis...
On a secant-like method for solving generalized equations
Ioannis K. Argyros, Said Hilout (2008)
Mathematica Bohemica
In the paper by Hilout and Piétrus (2006) a semilocal convergence analysis was given for the secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations). Here, we show that this convergence analysis can be refined under weaker hypothesis, and less computational cost. Moreover finer error estimates on the distances involved and a larger radius of convergence are obtained.
On an application of a Newton-like method to the approximation of implicit functions
Ioannis K. Argyros (1992)
Mathematica Slovaca
On iterative solution of nonlinear functional equations in a metric space.
Sen, Rabindranath, Mukherjee, Sulekha (1983)
International Journal of Mathematics and Mathematical Sciences
On mesh independence and Newton-type methods
Owe Axelsson (1993)
Applications of Mathematics
Mesh-independent convergence of Newton-type methods for the solution of nonlinear partial differential equations is discussed. First, under certain local smoothness assumptions, it is shown that by properly relating the mesh parameters and for a coarse and a fine discretization mesh, it suffices to compute the solution of the nonlinear equation on the coarse mesh and subsequently correct it once using the linearized (Newton) equation on the fine mesh. In this way the iteration error will be...
On monotone and Schwarz alternating methods for nonlinear elliptic PDEs
Shiu-Hong Lui (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...
On Monotone and Schwarz Alternating Methods for Nonlinear Elliptic PDEs
Shiu-Hong Lui (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...
On Multilevel Iterative Methods for Integral Equations of the Second Kind and Related Problems.
Jan Mandel (1985)
Numerische Mathematik
On multipoint iterative processes of efficiency index higher than Newton's method.
Argyros, Ioannis K., Hilout, Saïd (2009)
The Journal of Nonlinear Sciences and its Applications
On Newton-Like Methods.
J.E. jr. DENNIS (1968)
Numerische Mathematik
On numerical integration of implicit ordinary differential equations
Zdzisław Jackiewicz, Marian Kwapisz (1981)
Aplikace matematiky
In this paper it is shown how the numerical methods for ordinary differential equations can be adapted to implicit ordinary differential equations. The resulting methods are of the same order as the corresponding methods for ordinary differential equations. The convergence theorem is proved and some numerical examples are given.
On polynomial equations in Banach space, perturbation techniques and applications.
Argyros, Ioannis K. (1987)
International Journal of Mathematics and Mathematical Sciences
On the application of Newton's and chord methods of bifurcation problems.
Elgindi, M.B.M. (1994)
International Journal of Mathematics and Mathematical Sciences
On the approximate solution of some Fredholm integral equations by Newton's method.
Gutiérrez, J.M., Hernández, M.A., Salanova, M.A. (2004)
Southwest Journal of Pure and Applied Mathematics [electronic only]
On the approximation of some nonlinear equations.
Ioannis K. Argyros (1987)
Aequationes mathematicae
On the Approximative Roots of Maximal Monotone Mappings
L. D. Popov (1996)
The Yugoslav Journal of Operations Research
On the Chaplyghin method for generalized solutions of partial differential functional equations.
Czernous, Wojciech (2005)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
On the computation of nonhyperbolic fixed points.
Graça, Mário M. (2002)
Experimental Mathematics
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