General approach to constructing optimal multipoint families of iterative methods using Hermites rational interpolation Academic Article uri icon


  • 2017 Elsevier B.V. We discuss accelerating convergence of multipoint iterative methods for solving scalar equations, using particular type rational interpolant. Both derivative-free and Newton-type methods are investigated simultaneously. As a conclusion a Theorem of Knig's type for multipoint iterations is stated. A new optimal multipoint family of methods based on rational interpolation is constructed. The iteration uses n function evaluations per cycle and O(j) operations in jth step of a single iteration to obtain 2n1 order of convergence. Several equivalent forms of the obtained iterates and development techniques are presented.

published proceedings

  • Journal of Computational and Applied Mathematics

author list (cited authors)

  • Duni, J., & Damnjanovi, I.

citation count

  • 0

complete list of authors

  • Džunić, Jovana||Damnjanović, Ivan

publication date

  • September 2017