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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Approximate zeros of quadratically convergent algorithms
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by Pengyuan Chen PDF
Math. Comp. 63 (1994), 247-270 Request permission

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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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 63 (1994), 247-270
  • MSC: Primary 65H05; Secondary 65E05, 65Y20
  • DOI: https://doi.org/10.1090/S0025-5718-1994-1240655-0
  • MathSciNet review: 1240655