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Mathematics of Computation

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Approximate zeros of quadratically convergent algorithms

Author: Pengyuan Chen
Journal: Math. Comp. 63 (1994), 247-270
MSC: Primary 65H05; Secondary 65E05, 65Y20
MathSciNet review: 1240655
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Abstract: Smale’s condition for a point to be an approximate zero of a function for Newton’s method is extended to the general quadratically convergent iterative algorithm. It is shown in which way the bound in the condition is affected by the characteristics of the algorithm. This puts the original condition of Smale for Newton’s method in a more general perspective. The results are also discussed in the light of numerical evidence.

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Article copyright: © Copyright 1994 American Mathematical Society