Newton-Kantorovich Convergence Theorem of a Modified Newton's Method Under the Gamma-Condition in a Banach Space


CHEN M., KHAN Y., WU Q., Yildirim A.

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, cilt.157, ss.651-662, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 157 Konu: 3
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1007/s10957-012-0237-9
  • Dergi Adı: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • Sayfa Sayıları: ss.651-662

Özet

A Newton-Kantorovich convergence theorem of a modified Newton's method having third order convergence is established under the gamma-condition in a Banach space to solve nonlinear equations. It is assumed that the nonlinear operator is twice Fr,chet differentiable and satisfies the gamma-condition. We also present the error estimate to demonstrate the efficiency of our approach. A comparison of our numerical results with those obtained by other Newton-Kantorovich convergence theorems shows high accuracy of our results.