A Generic Family of Optimal Sixteenth-Order Multiple-Root Finders and Their Dynamics Underlying Purely Imaginary Extraneous Fixed Points

Min-Young Lee, Young Ik Kim and Beny Neta
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Min-Young Lee: Department of Applied Mathematics, Dankook University, Cheonan 330-714, Korea
Young Ik Kim: Department of Applied Mathematics, Dankook University, Cheonan 330-714, Korea
Beny Neta: Naval Postgraduate School, Department of Applied Mathematics, Monterey, CA 93943, USA

Mathematics, 2019, vol. 7, issue 6, 1-26

Abstract: A generic family of optimal sixteenth-order multiple-root finders are theoretically developed from general settings of weight functions under the known multiplicity. Special cases of rational weight functions are considered and relevant coefficient relations are derived in such a way that all the extraneous fixed points are purely imaginary. A number of schemes are constructed based on the selection of desired free parameters among the coefficient relations. Numerical and dynamical aspects on the convergence of such schemes are explored with tabulated computational results and illustrated attractor basins. Overall conclusion is drawn along with future work on a different family of optimal root-finders.

Keywords: sixteenth-order optimal convergence; multiple-root finder; asymptotic error constant; weight function; purely imaginary extraneous fixed point; attractor basin (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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