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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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