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Partial Fraction Expansions for Newton`s and Halley`s Iterations for Square Roots
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  • Journal title : Kyungpook mathematical journal
  • Volume 52, Issue 3,  2012, pp.347-357
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2012.52.3.347
 Title & Authors
Partial Fraction Expansions for Newton`s and Halley`s Iterations for Square Roots
Kouba, Omran;
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When Newton`s method, or Halley`s method is used to approximate the pth root of 1-z, a sequence of rational functions is obtained. In this paper, a beautiful formula for these rational functions is proved in the square root case, using an interesting link to Chebyshev`s polynomials. It allows the determination of the sign of the coefficients of the power series expansion of these rational functions. This answers positively the square root case of a proposed conjecture by Guo(2010).
Newton`s method;Halley`s method;Series expansion;Square roots;Chebyshev`s Polynomials;
 Cited by
The dual Padé families of iterations for the matrix pth root and the matrix p-sector function, Journal of Computational and Applied Mathematics, 2014, 272, 468  crossref(new windwow)
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