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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
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2157252
Page Count: 16
You can always find the topics here!Topics: Newtons method, Mathematical intervals, Nickel, Radii of convergence, Mathematical functions, Lipschitz condition, Real numbers, Newton approximation methods, Zero, Mathematical sequences
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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.
SIAM Journal on Numerical Analysis © 1981 Society for Industrial and Applied Mathematics