AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
Rezumat articol ediţie STUDIA UNIVERSITATIS BABEŞ-BOLYAI
În partea de jos este prezentat rezumatul articolului selectat. Pentru revenire la cuprinsul ediţiei din care face parte acest articol, se accesează linkul din titlu. Pentru vizualizarea tuturor articolelor din arhivă la care este autor/coautor unul din autorii de mai jos, se accesează linkul din numele autorului.
Autori: .
Published Online: 2017-03-03
Published Print: 2017-03-31
VIEW PDF: BALL CONVERGENCE OF A STABLE FOURTH-ORDER FAMILY FOR SOLVING NONLINEAR SYSTEMS UNDER WEAK CONDITIONS
We present a local convergence analysis of fourth-order methods in order to approximate a locally unique solution of a nonlinear equation in Banach space setting. Earlier studies have shown convergence using Taylor expansions and hypotheses reaching up to the fifth derivative although only the first derivative appears in these methods. We only show convergence using hypotheses on the first derivative. We also provide computable: error bounds, radii of convergence as well as uniqueness of the solution with results based on Lipschitz constants not given in earlier studies. The computational order of convergence is also used to determine the order of convergence. Finally, numerical examples are also provided to show that our results apply to solve equations in cases where earlier studies cannot apply.
Mathematics Subject Classification (2010): 65D10, 65D99.
Keywords: Local convergence, nonlinear equation, Lipschitz condition, Fréchet derivative.
