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A New Acceleration Method for Newton's Method at Singular Points
C. T. Kelley and R. Suresh
SIAM Journal on Numerical Analysis
Vol. 20, No. 5 (Oct., 1983), pp. 1001-1009
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2157113
Page Count: 9
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When Newton's method is used to find a root of a map from a Banach space into itself and the derivative is singular at that root, convergence of the Newton sequence is in general linear. In this paper we give a modification of Newton's method that, under certain conditions, converges superlinearly. Our method is applicable under more general conditions than other techniques. In particular it may be used for certain quadratic problems and problems in which the dimension of the null space of the derivative is larger than one.
SIAM Journal on Numerical Analysis © 1983 Society for Industrial and Applied Mathematics