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Convergence analysis of a family of Steffensen-type methods for generalized equations

Hilout, Saïd

Journal of mathematical analysis and applications, 2008-03, Vol.339 (2), p.753-761 [Periódico revisado por pares]

San Diego, CA: Elsevier Inc

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  • Título:
    Convergence analysis of a family of Steffensen-type methods for generalized equations
  • Autor: Hilout, Saïd
  • Assuntos: Aubin continuity ; Divided difference ; Exact sciences and technology ; Functional analysis ; Generalized equation ; Global analysis, analysis on manifolds ; Mathematical analysis ; Mathematics ; Regula-falsi method ; Sciences and techniques of general use ; Secant method ; Set-valued mapping ; Steffensen's method ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds ; ω-Conditioned divided difference
  • É parte de: Journal of mathematical analysis and applications, 2008-03, Vol.339 (2), p.753-761
  • Descrição: A class of Steffensen-type algorithms for solving generalized equations on Banach spaces is proposed. Using well-known fixed point theorem for set-valued maps [A.L. Dontchev, W.W. Hager, An inverse function theorem for set-valued maps, Proc. Amer. Math. Soc. 121 (1994) 481–489] and some conditions on the first-order divided difference, we provide a local convergence analysis. We also study the perturbed problem and we present a new regula-falsi-type method for set-valued mapping. This study follows the works on the Secant-type method presented in [S. Hilout, A uniparametric Secant-type methods for nonsmooth generalized equations, Positivity (2007), submitted for publication; S. Hilout, A. Piétrus, A semilocal convergence of a Secant-type method for solving generalized equations, Positivity 10 (2006) 673–700] and extends the results related to the resolution of nonlinear equations [M.A. Hernández, M.J. Rubio, The Secant method and divided differences Hölder continuous, Appl. Math. Comput. 124 (2001) 139–149; M.A. Hernández, M.J. Rubio, Semilocal convergence of the Secant method under mild convergence conditions of differentiability, Comput. Math. Appl. 44 (2002) 277–285; M.A. Hernández, M.J. Rubio, ω-Conditioned divided differences to solve nonlinear equations, in: Monogr. Semin. Mat. García Galdeano, vol. 27, 2003, pp. 323–330; M.A. Hernández, M.J. Rubio, A modification of Newton's method for nondifferentiable equations, J. Comput. Appl. Math. 164/165 (2004) 323–330].
  • Editor: San Diego, CA: Elsevier Inc
  • Idioma: Inglês
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