APPROXIMATING SOLUTIONS OF EQUATIONSBY COMBINING NEWTON-LIKE METHODS
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초록
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.
Abstract
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.
참고문헌 (7)
- Argyros, I.K., "A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space", J. Math. Anal. Appl, 298(2), pp.374~397 (2004)
- Argyros, I.K., "Approximate solution of operator equations with applications" (2005), World Scientific Publ. Co.
- Dennis, J.E., Jr., "On Newton-like methods", Numer. Math, 11, pp.324~330 (1968)
- Deuflhard, P., "Affine invariant convergence theorems for Newton's method and extensions to related methods", SIAM J. Numer. Anal, 16, pp.1~10 (1979)
- Kantorovich, L.V., "Functional Analysis in Normed Spaces" (1982), Pergamon Press
- Ortega, J.M., "Iterative solution of nonlinear equations in several variables" (1970), Academic Press
- Yamanoto, T., "A convergence theorem for Newton-like methods in Banach spaces", Numer. Math, 51, pp.545~557 (1987)