Parameter-based algorithms for approximating local solution of nonlinear complex equations
DOI:
https://doi.org/10.22199/S07160917.1994.0001.00007Keywords:
Nonlinear equations, Halley- Werner type methods, Ostrowski-Kantorovich analysis, Upper error boundAbstract
We study the Ostrowski-Kantorovich convergence for a family of Halley- Werner type iteration methods in the complex plane. We provide an upper error bound for all parameter ? ? [1 , 2). We show that the error bound is a decreasing function of ?. We prove also that the Halley method has the largest error bound.
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References
[1] E. Halley, A New Exact and Easy Method of Finding the Roots of equations Generally and that Without any Previous Reduction, Phil. Trans. Roy. London, 18(1694), 134-145.
[2] W. B. Gragg and R.A. Tapia, Optimal Error Bounds for the Newton-Kantorovich Theorem, SIAM J. Numer.Anal., 11(1974), 10-13.
[3] L.V. Kantorovich and G.P. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, New York, 1977.
[4] A.M. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, Third Edition, New York, 1973.
[5] W. Werner, Some Improvements of Classical Iterative Methods for the Solutions of Nonlinear Equations, Lecture Notes in Mathematics, Numerical Solution of Nonlinear Equations, Proceedings, Bremen, 878( 1980), 427-440.
[2] W. B. Gragg and R.A. Tapia, Optimal Error Bounds for the Newton-Kantorovich Theorem, SIAM J. Numer.Anal., 11(1974), 10-13.
[3] L.V. Kantorovich and G.P. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, New York, 1977.
[4] A.M. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, Third Edition, New York, 1973.
[5] W. Werner, Some Improvements of Classical Iterative Methods for the Solutions of Nonlinear Equations, Lecture Notes in Mathematics, Numerical Solution of Nonlinear Equations, Proceedings, Bremen, 878( 1980), 427-440.
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Published
2018-04-03
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How to Cite
[1]
“Parameter-based algorithms for approximating local solution of nonlinear complex equations”, Proyecciones (Antofagasta, On line), vol. 13, no. 1, pp. 53–61, Apr. 2018, doi: 10.22199/S07160917.1994.0001.00007.
