A new form of Kantorovich's Theorem for the method of Newton
DOI:
https://doi.org/10.21754/tecnia.v23i1.69Keywords:
Linear operator, Differentiable Fréchet, Convergent succession, UniquenessAbstract
A new Kantorovich-type convergence theorem for Newton’s method is established for approximating a locally unique solution of an equation F (x) = 0 defined on a Banach space. It is assumed that the operator F is twice Fre´chet differentiable, and that Fr, F rr satisfy Lipschitz conditions. Our convergence condition differs from earlier ones and therefore it has theoretical and practical value.
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[1] Argyros, I. K., “Newton-like methods under milddifferentiability conditions with error analysis”, Bull.Austral. Math. Soc.37(1988), 131-147.
[2] Argyros, I. K. and Szidarovszky F., “The Theory andApplications of Iteration Methods”, C.R.C. Press, Bo-ca Raton, Fla., 1993.
[3] Guti ́errez, J. M., “A new semilocal convergencetheorem for Newtons method”, J. Comput. Appl.Math.79(1997), 131-145.
[4] Guti ́errez, J. M., Hern ́andez, M. A. and Salanova,M. A., “Accessibility of solutions by Newton’s met-hod”, Internat. J. Comput. Math57(1995), 239-247.
[5] Huang, Z.“A note on the Kantorovick theorem forNewton iteration”, J. Comput. Appl. Math.47(1993)211-217.
[6] Kantorovich, L.V. and Akilov, G.P.“FunctionalAnalysis”, Pergamon Press, Oxford, 1982.
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