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International Journal of Computer Mathematics Volume 87, 2010 - Issue 15
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Section B

Semilocal convergence of a family of third-order Chebyshev-type methods under a mild differentiability condition

P. K. Parida Department of Mathematics, Indian Institute of Technology, Gandhinagar, 382424, IndiaCorrespondence[email protected]
&
D. K. Gupta Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India
Pages 3405-3419 | Received 15 Sep 2008, Accepted 03 May 2009, Published online: 16 Sep 2010

References

  • Candela , V. and Marquina , A. 1990 . Recurrence relations for rational cubic methods II: The Chebyshev method . Computing , 45 : 355 – 367 .
  • Ezquerro , J. A. and Hernández , M. A. 2005 . On the R-order of the Halley method . J. Math. Anal. Appl. , 303 : 591 – 601 .
  • Ganesh , M. and Joshi , M. C. 1991 . Numerical solvability of Hammerstein integral equations of mixed type . IMA J. Numer. Anal. , 11 : 21 – 31 .
  • Gutiérrez , J. M. and Hernández , M. A. 1998 . Recurrence relations for the super-Halley method . Comput. Math. Appl. , 36 : 1 – 8 .
  • Hernández , M. A. 1998 . Reduced recurrence relations for the Chebyshev method . J. Optim. Theory Appl. , 98 : 385 – 397 .
  • Hernández , M. A. 2000 . Second-derivative-free variant of the Chebyshev method for nonlinear equations . J. Optim. Theory Appl. , 104 : 501 – 515 .
  • Hernández , M. A. 2001 . Chebyshev's approximation algorithms and applications . Comput. Math. Appl. , 41 : 433 – 445 .
  • Hernández , M. A. and Romero , N. 2005 . On a new multiparametric family of Newton-like methods . Appl. Numer. Anal. Comput. Math. , 2 : 78 – 88 .
  • Hernández , M. A. and Romero , N. 2007 . General study of iterative processes of R-order at least three under weak convergence conditions . J. Optim. Theory Appl. , 133 : 163 – 177 .
  • Hernández , M. A. and Salanova , M. A. 2000 . Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method . J. Comput. Appl. Math. , 126 : 131 – 143 .
  • Kantorovich , L. V. and Akilov , G. P. 1982 . Functional Analysis , Oxford : Pergamon Press .
  • Lambert , J. D. 1979 . Computational Methods in Ordinary Differential Equations , New York : Wiley .
  • Ortega , J. M. and Rheinboldt , W. C. 1970 . Iterative Solution of Nonlinear Equations in Several Variables , New York : Academic Press .
  • Ye , X. and Li , C. 2006 . Convergence of the family of the deformed Euler–Halley iterations under the Hölder condition of the second derivative . J. Comput. Appl. Math. , 194 : 294 – 308 .
  • Ye , X. , Li , C. and Shen , W. 2007 . Convergence of the variants of the Chebyshev–Halley iteration family under the Hölder condition of the first derivative . J. Comput. Appl. Math. , 203 : 279 – 288 .

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