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Optimal Order Iterative Methods
  • xiang li,
  • xue Wang,
  • jia Wei
xiang li
Harbin University of Science and Technology

Corresponding Author:[email protected]

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xue Wang
Harbin University of Science and Technology
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jia Wei
Harbin University of Science and Technology
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Abstract

Based on Newton’s method and interpolation method, we establish two iterative methods for solving the nonlinear equations by using n+1 evaluations of the function(or the first derivative) per iteration. Analysis of convergence shows that our methods arrive at the optimal order of convergence 2^n, where the n is any a nature number. This work also proves the conjecture of Kung-Traub (J.ACM643-651,1974) for constructing multipoint optimal iterations.