Unified Convergence Analysis of Chebyshev–Halley Methods for Multiple Polynomial Zeros

Stoil I. Ivanov
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Stoil I. Ivanov: Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria

Mathematics, 2022, vol. 10, issue 1, 1-12

Abstract: In this paper, we establish two local convergence theorems that provide initial conditions and error estimates to guarantee the Q -convergence of an extended version of Chebyshev–Halley family of iterative methods for multiple polynomial zeros due to Osada ( J. Comput. Appl. Math. 2008, 216 , 585–599). Our results unify and complement earlier local convergence results about Halley, Chebyshev and Super–Halley methods for multiple polynomial zeros. To the best of our knowledge, the results about the Osada’s method for multiple polynomial zeros are the first of their kind in the literature. Moreover, our unified approach allows us to compare the convergence domains and error estimates of the mentioned famous methods and several new randomly generated methods.

Keywords: iteration methods; Chebyshev–Halley family; polynomial zeros; multiple zeros; local convergence; error estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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