Open AccessSome optimal iterative methods and their with memory variants
Author(s) -
Fazlollah Soleymani
Publication year - 2013
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.01.002
Subject(s) - mathematics , extension (predicate logic) , multiplicity (mathematics) , algorithm , iterative method , series (stratigraphy) , mathematical optimization , order (exchange) , computer science , mathematical analysis , paleontology , finance , economics , biology , programming language
Based on the fourth-order method of Liu et al. [10], eighth-order three-step iterative methods without memory, which are totally free from derivative calculation and reach the optimal efficiency index are presented. The extension of one of the methods for multiple zeros without the knowledge of multiplicity is presented. Further accelerations will be provided through the concept of with memory iteration methods. Moreover, it is shown by way of illustration that the novel methods are useful on a series of relevant numerical problems when high precision computing is required