INEXACT NEWTON METHODS

作者: Ron S. Dembo , Stanley C. Eisenstat , Trond Steihaug

DOI: 10.1137/0719025

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摘要: A classical algorithm for solving the system of nonlinear equations $F(x) = 0$ is Newton’s method \[ x_{k + 1} x_k s_k ,\quad {\text{where }}F'(x_k )s_k - F(x_k ),\quad x_0 {\text{ given}}.\]...

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James M. Ortega, Werner C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables ,(1970)
J. E. Dennis, Jorge J. Mor{é, A Characterization of Superlinear Convergence and its Application to Quasi-Newton Methods Mathematics of Computation. ,vol. 28, pp. 549- 560 ,(1973) , 10.1090/S0025-5718-1974-0343581-1