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RESEARCH PRODUCT
A class of quasi-Newton generalized Steffensen methods on Banach spaces
Sonia BusquierVicente F. CandelaSergio Amatsubject
SequenceClass (set theory)Applied MathematicsMathematical analysisBanach spaceKantarovich conditionsType (model theory)Nonlinear equationsGeneralized Steffensen methodsSteffensen's methodNonlinear systemComputational MathematicsConvergence (routing)Applied mathematicsQuasi-Newton methodMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-12-01 | Journal of Computational and Applied Mathematics |