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A Globally Convergent Ball Newton Method

Karl L. Nickel
SIAM Journal on Numerical Analysis
Vol. 18, No. 6 (Dec., 1981), pp. 988-1003
Stable URL: http://www.jstor.org/stable/2157252
Page Count: 16
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A Globally Convergent Ball Newton Method
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Abstract

A new n-dimensional Newton method is presented. In each step a whole n-dimensional ball is determined rather than a single new approximation point. This ball contains the desired zero of the given function. The method is globally convergent. If the given initial ball does not contain any zero, then the method stops after a finite number of steps. Depending upon the assumptions which are made, the convergence of the ball radii is linear, superlinear or quadratic.

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