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Original Articles

A family of one-point iteration formulae for finding roots

Pages 85-88 | Received 01 Mar 1979, Published online: 19 Mar 2007

References

  • Halley , E. 1964 . A new, exact and easy method of finding the roots of equations generally,and that without any previous reduction . Phil. Trans. Roy. Soc.London , 18 : 136 – 145 .
  • Traub , J.F. 1964 . Iterative Methods for the Solution of Equations , Englewood-Cliffs, New Jersey : Prentice-Hall .
  • Salehov , G.S. 1952 . On the convergence of the process of tangent hyperbolas (Russian) . Doklady Akad. Nauk SSSR , 82 : 525 – 528 .
  • Davies , M. and Dawson , B. 1975 . On the global convergence of Halley's iteration formula . Numer. Math , 24 : 133 – 135 .
  • Hansen , E. and Patrick , M. 1977 . A family of root finding methods . Numer. Math , 27 : 257 – 269 .
  • Berezin , I.S. and Zidkov , N.P. 1960 . Computational Methods (Russian) , Vol. 2 , Moscow : Gosudarstv. Izdat. Fiz.-Mat. Lit .
  • Sendov , B. and Popov , V. 1976 . Computational Methods (Bulgarian) , Vol. 1 , Sophia : Izdat. Nauka i Izkustvo .
  • Cauchy , A. 1899 . “ Sur la Determination Approximative des Racines d'une Équation Algebriqueou Transcendante ” . In Oeuvres Complètes , Vol. 4 , 573 – 609 . Paris : Gauthier–Villars . Série 2
  • Hitotumatu , S. 1962 . A method of successive approximation based on the expansion of second order . Math.Japon , 7 : 31 – 50 .
  • Ostrowski , A.M. 1973 . “ Solution of equations in Euclidean and Banach spaces ” . In Solution of Equations and Systems of Equations , New York : Academic Press . London

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