On optimal parameter of Laguerre’s family of zero-finding methods
MetadataShow full item record
A one parameter Laguerre’s family of iterative methods for solving nonlinear equations is considered. This family includes the Halley, Ostrowski and Euler methods, most frequently used one-point third-order methods for finding zeros. Investigation of convergence quality of these methods and their ranking is reduced to searching optimal parameter of Laguerre’s family, which is the main goal of this paper. Although methods from Laguerre’s family have been extensively studied in the literature for more decades, their proper ranking was primarily discussed according to numerical experiments. Regarding that such ranking is not trustworthy even for algebraic polynomials, more reliable comparison study is presented by combining the comparison by numerical examples and the comparison using dynamic study of methods by basins of attraction that enable their graphic visualization. This combined approach has shown that Ostrowski’s method possesses the best convergence behaviour for most polynomial equations.
The article of record as published may be found at http://doi.org/10.1080/00207160.2018.1429598
Showing items related by title, author, creator and subject.
Neta, Beny; Chun, Changbum (2013);There are several methods for solving a nonlinear algebraic equation having roots of a given multiplicity m. Here we compare a family of Laguerre methods of order three as well as two others of the same order and show that ...
Chun, Changbum; Neta, Beny (Springer, 2016);Recently Lotfi et al. (Numer. Algor. 68, 261-288, 2015) have developed a new family of optimal order eight for the solution of nonlinear equations. they have experimented with 3 members of the family and compared them to ...
Stewart, Bart D. (Monterey, California. Naval Postgraduate School, 2001-06);Real world phenomena commonly exhibit nonlinear relationships, complex geometry, and intricate processes. Analytic or exact solution methods only address a minor class of such phenomena. Consequently, numerical approximation ...