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作者:J.A. Ezquerro , M.A. Hernández , M.A. Salanova
来源:[J].Journal of Computational and Applied Mathematics(IF 0.989), 2000, Vol.115 (1), pp.181-192
摘要:Abstract(#br)We approximate a locally unique solution of an equation in Banach spaces using a Newton-like method of R -order three. Then we apply this method to obtain an existence-uniqueness result for a basic conservative problem given by a nonlinear boundary-value problem. Nex...
作者:... J.M. Gutiérrez , M.A. Hernández , M.A. Salanova
来源:[J].Computers and Mathematics with Applications(IF 2.069), 1998, Vol.36 (4), pp.9-20
摘要:Abstract(#br)We consider an inverse-free Jarratt-type approximation, whose order of convergence is four, for solving nonlinear equations. The convergence of this method is analysed under two different types of conditions. We use a new technique based on constructing a system of r...
作者:M.A. Hernández , M.A. Salanova
来源:[J].Applied Mathematics and Computation(IF 1.349), 1999, Vol.103 (1), pp.27-49
摘要:Abstract(#br)We define an index to measure the convexity of a convex function f at each point. We use this index to establish conditions on the convergence of the Halley method in the complex plane and in Banach spaces.
作者:M.A. Hernández , M.A. Salanova
来源:[J].Journal of Computational and Applied Mathematics(IF 0.989), 2000, Vol.126 (1), pp.131-143
摘要:Abstract(#br)This study obtains two semilocal convergence results for the well-known Chebyshev method, which is a third-order iterative process. The hypotheses required are modifications to the normal Kantorovich ones. The results obtained are applied to the reduction of nonlinea...
作者:J.A. Ezquerro , M.A. Hernández , M.A. Salanova
来源:[J].Journal of Computational and Applied Mathematics(IF 0.989), 1998, Vol.98 (2), pp.305-309
摘要:Abstract(#br)We establish a convergence theorem for the Midpoint method using a new system of recurrence relations. The purpose of this note is to relax its convergence conditions. We also given an example where our convergence theorem can be applied but other ones cannot.
作者:M.A. Hernández , M.A. Salanova
来源:[J].Applied Mathematics and Computation(IF 1.349), 1998, Vol.95 (1), pp.51-62
摘要:Abstract(#br)From convexity we obtain new convergence theorems for the Chebyshev method applied to a nonlinear scalar equation f ( x ) = 0. Moreover, Kantorovich type conditions for the convergence of the Chebyshev method in the complex plane are given. Finally, a new type of ass...
作者:J.M. Gutierrez , M.A. Hernandez , M.A. Salanova
来源:[J].Numerical Functional Analysis and Optimization(IF 0.5), 1996, Vol.17 (1-2), pp.113-121
摘要:A new convergence theorem is established for the super-Halley method. This method has, in general, order three, but when it is applied to quadratic equations, its order is four.

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