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Semilocal Convergence Analysis for Inexact Newton Method under Weak Condition

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  • Xiubin Xu
  • Yuan Xiao
  • Tao Liu

Abstract

Under the hypothesis that the first derivative satisfies some kind of weak Lipschitz conditions, a new semilocal convergence theorem for inexact Newton method is presented. Unified convergence criteria ensuring the convergence of inexact Newton method are also established. Applications to some special cases such as the Kantorovich type conditions and γ‐Conditions are provided and some well‐known convergence theorems for Newton′s method are obtained as corollaries.

Suggested Citation

  • Xiubin Xu & Yuan Xiao & Tao Liu, 2012. "Semilocal Convergence Analysis for Inexact Newton Method under Weak Condition," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:982925
    DOI: 10.1155/2012/982925
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