98
Views
0
CrossRef citations to date
0
Altmetric
Section B

Inverse function, Taylor's expansion and extended Schröder's processes

&
Pages 1281-1298 | Received 09 Jan 2013, Accepted 07 Aug 2013, Published online: 29 Nov 2013

References

  • D.F. Bateman, A historical survey of solution by functional iteration, Math. Mag. 62 (1989), pp. 155–166. doi: 10.2307/2689923
  • F. Dubeau, Algorithms for nth root approximation, Computing 57 (1996), pp. 365–369. doi: 10.1007/BF02252255
  • F. Dubeau, Newton's method and high-order algorithms for the nth root computation, J. Comput. Appl. Math. 224 (2009), pp. 66–76. doi: 10.1016/j.cam.2008.04.014
  • E. Durand, Solutions numériques des équations algébriques, Tome 1, Masson et Cie, Paris, 1960.
  • C.T. Fike, Computer Evaluation of Mathematical Functions, Prentice-Hall, Englewood Cliffs, NJ, 1968.
  • J. Gerlach, Accelerated convergence in Newton's method, SIAM Rev. 36 (1994), pp. 272–276. doi: 10.1137/1036057
  • J.M. Gutierrez, M.A. Hernandez, and M.A. Solanova, Calculus of nth roots and third order iterative methods, Nonlinear Anal. 47 (2001), pp. 2875–2880. doi: 10.1016/S0362-546X(01)00408-4
  • M.A. Hernandez and N. Romero, High order algorithms for approximating nth roots, Int. J. Comput. Math. 81 (2004), pp. 1001–1014. doi: 10.1080/00207160410001714583
  • M.A. Hernandez and N. Romero, Accelerated convergence in Newton's method for approximating square roots, J. Comput. Appl. Math. 177 (2005), pp. 225–229. doi: 10.1016/j.cam.2004.09.025
  • A.S. Househoulder, Principles of Numerical Analysis, McGraw-Hill, Columbus, OH, 1953.
  • K.R. Johnson, An iterative method for approximating square roots, Math. Mag. 62 (1989), pp. 253–259. doi: 10.2307/2689764
  • B. Kalantari, On the order of convergence of determinantal family of root-finding methods, BIT 39 (1999), pp. 96–109. doi: 10.1023/A:1022321325108
  • B. Kalantari and I. Kalantari, High order methods for approximating square roots, BIT 36 (1996), pp. 395–399. doi: 10.1007/BF01731991
  • D. Kincaid and W. Cheney, Numerical Analysis, Brooks/Cole Pub. Co., Pacific Grove, CA, 1991.
  • R.J. Knill, A modified Babylonian algorithm, Am. Math. Monthly 99 (1992), pp. 734–737. doi: 10.2307/2324239
  • J.-M. Müller, Elementary Functions: Algorithms and Implementation, Birkhaüser, Boston, MA, 1997.
  • A.Y. Özban, New methods for approximating square roots, Appl. Math. Comput. 175 (2006), pp. 532–540. doi: 10.1016/j.amc.2005.07.056
  • E. Schröder, Uber unendlich viele Algorithmen zur Auflosung der Gleichungen, Math. Ann. 2 (1870), pp. 317–365.
  • E. Schröder, On Infinitely Many Algorithms for Solving Equations, Translated by G.W. Stewart, Institute for advanced Computer Studies, TR-92-121 and TR-2990, University of Maryland, College Park, MD, 1992.
  • J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 2nd ed., Springer-Verlag, New York, 1993.
  • J.F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, NJ, 1964.
  • A.K. Yeyios, On two sequences of algorithms for approximating square roots, J. Comput. Appl. Math. 40 (1992), pp. 63–72. doi: 10.1016/0377-0427(92)90042-V

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.