General Local Convergence Theorems about the Picard Iteration in Arbitrary Normed Fields with Applications to Super–Halley Method 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, 2020, vol. 8, issue 9, 1-11

Abstract: In this paper, we prove two general convergence theorems with error estimates that give sufficient conditions to guarantee the local convergence of the Picard iteration in arbitrary normed fields. Thus, we provide a unified approach for investigating the local convergence of Picard-type iterative methods for simple and multiple roots of nonlinear equations. As an application, we prove two new convergence theorems with a priori and a posteriori error estimates about the Super-Halley method for multiple polynomial zeros.

Keywords: iterative methods; local convergence; error estimates; normed fields; Super-Halley method; polynomial zeros; multiple zeros (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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