Search results for "Steffensen's method"

showing 2 items of 2 documents

The convergence of the perturbed Newton method and its application for ill-conditioned problems

2011

Abstract Iterative methods, such as Newton’s, behave poorly when solving ill-conditioned problems: they become slow (first order), and decrease their accuracy. In this paper we analyze deeply and widely the convergence of a modified Newton method, which we call perturbed Newton, in order to overcome the usual disadvantages Newton’s one presents. The basic point of this method is the dependence of a parameter affording a degree of freedom that introduces regularization. Choices for that parameter are proposed. The theoretical analysis will be illustrated through examples.

Mathematical optimizationIterative methodApplied MathematicsSteffensen's methodNewton's method in optimizationLocal convergenceComputational Mathematicssymbols.namesakeNonlinear systemNewton fractalSecant methodsymbolsNewton's methodMathematicsApplied Mathematics and Computation
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A class of quasi-Newton generalized Steffensen methods on Banach spaces

2002

AbstractWe consider a class of generalized Steffensen iterations procedure for solving nonlinear equations on Banach spaces without any derivative. We establish the convergence under the Kantarovich–Ostrowski's conditions. The majorizing sequence will be a Newton's type sequence, thus the convergence can have better properties. Finally, a numerical comparation with the classical methods is presented.

SequenceClass (set theory)Applied MathematicsMathematical analysisBanach spaceKantarovich conditionsType (model theory)Nonlinear equationsGeneralized Steffensen methodsSteffensen's methodNonlinear systemComputational MathematicsConvergence (routing)Applied mathematicsQuasi-Newton methodMathematicsJournal of Computational and Applied Mathematics
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