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;
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).