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International Journal of Computer Mathematics Volume 97, 2020 - Issue 1-2: Selected papers of CMMSE: Computational and Mathematical methods in Science Engineering and Economics
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Original Articles

An alternative analysis for the local convergence of iterative methods for multiple roots including when the multiplicity is unknown

Diego AlarcónDepartamento de Matemática Aplicada, Universitat Politècnica de València, Valencia, SpainCorrespondence[email protected]
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,
Jose L. HuesoInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, SpainView further author information
&
Eulalia MartínezInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, SpainView further author information
Pages 312-329 | Received 14 Sep 2018, Accepted 23 Dec 2018, Published online: 24 Mar 2019

References

  • D. Alarcón, F. Cevallos, J.L. Hueso, and E. Martínez, A comparative study of the local convergence radius of iterative methods for multiple roots, Model Eng Human Behavior (2017), pp. 1–6.
  • Tom M. Apostol, One-Variable Calculus, with an Introduction to Lineal Algebra, Blaisdell, Waltham, MA, 1967.
  • I. Argyros, On the convergence and application of Newton's method under weak Hölder continuity assumptions, Int. J. Comput. Math. 80 (2003), pp. 767–780. doi: 10.1080/0020716021000059160
  • W. Bi, H. Ren, and Q. Wu, Convergence of the modified Halley's method for multiple zeros under Hölder continuous derivative, Numer. Alg. 58 (2011), pp. 497–512. doi: 10.1007/s11075-011-9466-5
  • C. Dong, A basic theorem of constructing an iterative formula of the higher order for computing multiple roots of an equation, Math. Numer. Sin. 11 (1982), pp. 445–450.
  • Jose L. Hueso, E. Martínez, and C. Teruel, Determination of multiple roots of nonlinear equations and applications, J. Math. Chem. 53 (2015), pp. 880–892. doi: 10.1007/s10910-014-0460-8
  • J.M. McNamee, A comparison of methods for accelerating convergence of Newton's method for multiple polynomial roots, ACM SIGNUM Newslett. 33 (1998), pp. 17–22. doi: 10.1145/290590.290592
  • J. Ortega, Solution of equations in Euclidean and Banach spaces, SIAM Rev. 16 (1974), pp. 564–564. doi: 10.1137/1016102
  • N. Osada, An optimal multiple root-finding method of order three, J. Comput. Appl. Math. 51(1) (1994), pp. 131–133. doi: 10.1016/0377-0427(94)00044-1
  • E. Schröder, Ueber unendlich viele Algorithmen zur Auflösung der Gleichungen, Math. Ann. 16 (1870), pp. 317–365. doi: 10.1007/BF01444024
  • J.K. Traub, Iterative methods for the solution of equations, Math. Ann. 312 (1964), pp. 317–365.
  • M. Vander Straten and H. Van de Vel, Multiple root-finding methods, J. Comput. Appl. Math. 40 (1992), pp. 105–114. doi: 10.1016/0377-0427(92)90045-Y
  • X. Zhou, X. Chen, and Y. Song, On the convergence radius of the modified Newton method for multiple roots under the center-Hölder condition, Numer. Algorithms 65 (2014), pp. 221–232. doi: 10.1007/s11075-013-9702-2
  • X. Zhou and Y. Song, Convergence radius of Osada's method under center-Hölder continuous condition, Appl. Math. Comput. 243 (2014), pp. 809–816.

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