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Original Articles

R-order of convergence for the improved multi-point Chebyshev-like methods under generalized continuity condition

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Pages 906-919 | Received 05 Mar 2017, Accepted 30 Apr 2018, Published online: 09 Apr 2019

References

  • S. Amat, C. Bermúdez, S. Busquier, and S. Plaza, On a third-order Newton-type method free of bilinear operators, Numer. Linear Algebra Appl. 17 (2010), pp. 639–653.
  • I.K. Argyros and Á.A. Magreñán, Extending the applicability of the local and semilocal convergence of Newton's method, Appl. Math. Comput. 292 (2017), pp. 349–355.
  • D.D. Bruns and J.E. Bailey, Nonlinear feedback control for operating a nonisothermal CSTR near an unstable steady state, Chem. Eng. Sci. 32 (1977), pp. 257–264. doi: 10.1016/0009-2509(77)80203-0
  • C. Chun and B. Neta, Some modification of Newton's method by the method of undetermined coefficients, Comput. Math. Appl. 56 (2008), pp. 2528–2538. doi: 10.1016/j.camwa.2008.05.005
  • J.A. Ezquerro and M.A. Hernández, On the R-order of the Halley method, J. Math. Anal. Appl. 303 (2005), pp. 591–601. doi: 10.1016/j.jmaa.2004.08.057
  • M. Ganesh and M.C. Joshi, Numerical solvability of Hammerstein integral equations of mixed type, IMA J. Numer. Anal. 11 (1991), pp. 21–31. doi: 10.1093/imanum/11.1.21
  • D. Herceg and D. Herceg, On a third order family of methods for solving nonlinear equations, Int. J. Comput. Math. 87 (2010), pp. 2533–2541. doi: 10.1080/00207160802684434
  • M.A. Hernández, Second-derivative-free variant of the Chebyshev method for nonlinear equations, J. Optim. Theory Appl. 104(3) (2000), pp. 501–515. doi: 10.1023/A:1004618223538
  • M.A. Hernández and M.A. Salanova, Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method, J. Comput. Appl. Math. 126 (2000), pp. 131–143. doi: 10.1016/S0377-0427(99)00347-7
  • J. Kou, Y. Li, and X. Wang, A modification of Newton's method with third-order convergence, Appl. Math. Comput. 181 (2007), pp. 1106–1111.
  • E. Martínez, S. Singh, J.L. Hueso, and D.K. Gupta, Local convergence of a family of iterative methods for Hammerstein equations, J. Math. Chem. 54 (2016), pp. 1370–1386. doi: 10.1007/s10910-016-0602-2
  • J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equation in Several Variables, Academic Press, New York, 1970.
  • X. Wang and J. Kou, Semilocal convergence of multi-point improved super-Halley-type methods without the second derivative under generalized weak condition, Numer. Algorithms 71 (2016), pp. 567–584. doi: 10.1007/s11075-015-0010-x
  • X. Wang and J. Kou, Semilocal convergence on a family of root-finding multi-point methods in Banach spaces under relaxed continuity condition, Numer. Algorithms 74 (2017), pp. 643–657. doi: 10.1007/s11075-016-0165-0

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