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

abstract

• 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.

authors

• Damnjanovic, Ivan

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

publisher

• Elsevier BV  Publisher

published in

• Journal of Computational and Applied Mathematics  Journal

keywords

• Divided Difference
• Hermite Rational Interpolation
• Iterative Methods
• Nonlinear Equations

Digital Object Identifier (DOI)

• 10.1016/j.cam.2017.02.039

start page

• 261

end page

• 269

volume

• 321