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Original Articles

A family of Newton-like methods based on an exponential model

Pages 297-304 | Received 24 Apr 2006, Accepted 30 Oct 2006, Published online: 17 May 2007

References

  • Dennis , J. E. and Schnable , R. B. 1983 . Numerical Methods for Unconstrained Optimization and Nonlinear Equations , Englewood Cliffs, NJ : Prentice-Hall .
  • Jarratt , P. 1970 . A Review of Methods for Solving Nonlinear Algebraic Equations , London : Gordon & Breach .
  • Ostrowski , A. M. 1973 . Solution of Equations in Euclidean and Banach Space , New York : Academic Press .
  • Traub , J. F. 1964 . Iterative Methods for the Solution of Equations , Englewood Cliffs, NJ : Prentice-Hall .
  • Halley , E. 1694 . A new, exact and easy method of finding the roots of equations generally, and that without any previous reduction . Philosophical Transactions of the Royal Society of London , 18 : 136 – 145 .
  • Amat , S. , Busquier , S. and Gutíerrez , J. M. 2003 . Geometric constructions of iterative functions to solve nonlinear equations . Journal of Computational and Applied Mathematics , 157 : 197 – 205 .
  • Gutíerrez , J. M. and Hernández , M. A. 2001 . An acceleration of Newton's method: super-Halley method . Applied Mathematics and Computation , 117 : 223 – 239 .
  • Hernández , M. A. and Salanova , M. A. 1994 . A family of Newton type iterative processes . International Journal of Computer Mathematics , 51 : 205 – 214 .
  • Homeier , H. H.H. 2003 . A modified Newton method for rootfinding with cubic convergence . Journal of Computational and Applied Mathematics , 157 : 227 – 230 .
  • Martínez , J. M. 2000 . Practical quasi-Newton methods for solving nonlinear systems . Journal of Computational and Applied Mathematics , 124 : 97 – 121 .
  • Potra , F. A. and Pták , V. 1984 . Nondiscrete Induction and Iterative Processes. Research Notes in Mathematics , Vol. 103 , Boston, MA : Pitman .
  • Sharma , J. R. 2005 . A composite third order Newton–Steffensen method for solving nonlinear equations . Applied Mathematics and Computation , 169 : 242 – 246 .

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