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In cases su±cient conditions for the semilocal convergence of Newton-
like methods are violated, we start with a modi¯ed Newton-like method (whose
weaker convergence conditions hold) until we stop at a certain ¯nite step. Then
using as a starting guess the point found above we show convergence of the Newton-
like method to a locally unique solution of a nonlinear operator equation in a Banach
space setting. A numerical example is also provided.
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참고문헌 (7)
참고문헌 신청
Argyros, I.K. / 2004 / A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space / J. Math. Anal. Appl 298 (2) : 374
Argyros, I.K. / 2005 / Approximate solution of operator equations with applications / World Scientific Publ. Co.
Dennis, J.E., Jr. / 1968 / On Newton-like methods / Numer. Math 11 : 324 ~ 330
Deuflhard, P. / 1979 / Affine invariant convergence theorems for Newton's method and extensions to related methods / SIAM J. Numer. Anal 16 : 1 ~ 10
Kantorovich, L.V. / 1982 / Functional Analysis in Normed Spaces / Pergamon Press
Argyros, I.K. / 2005 / Approximate solution of operator equations with applications / World Scientific Publ. Co.
Dennis, J.E., Jr. / 1968 / On Newton-like methods / Numer. Math 11 : 324 ~ 330
Deuflhard, P. / 1979 / Affine invariant convergence theorems for Newton's method and extensions to related methods / SIAM J. Numer. Anal 16 : 1 ~ 10
Kantorovich, L.V. / 1982 / Functional Analysis in Normed Spaces / Pergamon Press
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