ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONS

ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONS

We use a two-step Steffensen-type method [1], [2], [4], [6], [13]-[16] to solve a generalized equation in a Banach space setting under Hölder-type conditions introduced by us in [2], [6] for nonlinear equations. Using some ideas given in [4], [6] for nonlinear equations, we provide a local convergen...

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Detalles Bibliográficos
Autores principales: ARGYROS,IOANNIS K, HILOUT,SAÏD
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2008
Materias:
Banach space
Steffensen’s method
generalized equation
Aubin continuity
Hölder continuity
radius of convergence
divided difference
set- valued map
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000300007
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Sumario:We use a two-step Steffensen-type method [1], [2], [4], [6], [13]-[16] to solve a generalized equation in a Banach space setting under Hölder-type conditions introduced by us in [2], [6] for nonlinear equations. Using some ideas given in [4], [6] for nonlinear equations, we provide a local convergence analysis with the following advantages over related [13]-[16]: finer error bounds on the distances involved, and a larger radius of convergence. An application is also provided.

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