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Section B

On the improved Newton-like methods for the inclusion of polynomial zeros

, &
Pages 1726-1735 | Received 12 Jun 2008, Accepted 02 Sep 2008, Published online: 22 Jun 2009

References

  • Carstensen , C. and Petković , M. S. 1994 . An improvement of Gargantini's simultaneous inclusion method for polynomial roots by Schroeder's correction . Appl. Numer. Math. , 25 : 59 – 67 .
  • Ehrlich , L. W. 1967 . A modified Newton method for polynomials . Commun. ACM , 10 : 107 – 108 .
  • Fousse , L. , Hanrot , G. , Lefèvre , V. , Pèlissier , P. and Zimmermann , P. 2007 . MPFR: a multi-precision binary floating-point library with correct rounding . ACM Trans. Math. Software , 33 article 13
  • Fujimoto , J. , Ishikawa , T. and Perret-Gallix , D. 2005 . High precision numerical computations . Tech. Rep. ACCP-N-1 ,
  • Gargantini , I. and Henrici , P. 1972 . Circular arithmetic and the determination of polynomial zeros . Numer. Math. , 18 : 305 – 320 .
  • Granlund , T. GNU MP; The GNU Multiple Precision Arithmetic Library , 2.0
  • Herzberger , J. and Metzner , L. 1996 . “ On the Q-order and R-order of convergence for coupled sequences arising in iterative numerical processes ” . In Numerical Methods and Error Bounds , Edited by: Alefeld , G. and Herzberger , J. 120 – 131 . Berlin : Mathematical Research 89, Akademie .
  • Jarratt , P. 1966 . Some fourth order multipoint methods for solving equations . Math. Comput. , 20 : 434 – 437 .
  • McNamee , J. M. 2007 . Numerical Methods for Roots of Polynomials, Part I , Amsterdam : Elsevier .
  • Nourein , A. W.M. 1997 . An improvement on two iteration methods for simultanneously determination of the zeros of a polynomial . Int. J. Comput. Math. , 6 : 241 – 252 .
  • Petković , I. 2008 . Computational efficiency of some combined methods for polynomial equations . App. Math. Comp. , 204 : 949 – 956 .
  • Petković , M. S. 1989 . Iterative Methods for Simultaneous Inclusion of Polynomial Zeros , Berlin : Springer . (Reprinted in 2008)
  • Petković , M. S. 1999 . Halley-like method with corrections for the inclusion of polynomial zeros . Computing , 62 : 69 – 88 .
  • Petković , M. S. 2008 . Point Estimation of Root Finding Methods , Berlin : Springer .
  • Petković , M. S. and Carstensen , C. 1993 . On some improved inclusion methods for polynomial roots with Weierstrass’ correction . Comput. Math. Appl. , 25 : 59 – 67 .
  • Petković , M. S. and Milovšević , D. 2004 . Ostrowski-like method with corrections for the inclusion of polynomial zeros . Reliab. Comput. , 10 : 437 – 467 .
  • Petković , M. S. and Milovšević , D. 2006 . On a new family of simultaneous methods with corrections for the inclusion of polynomial zeros . Int. J. Comput. Math. , 83 : 299 – 317 .
  • Petković , M. S. and Petković , L. D. 1998 . Complex Interval Arithmetic and its Applications , Berlin : Wiley-VCH .
  • Smith , D. M. 1998 . Multiple precision complex arithmetic and functions . ACM Trans. Math. Software , 24 : 359 – 367 .

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