General Local Convergence Theorems about the Picard Iteration in Arbitrary Normed Fields with Applications to Super–Halley Method for Multiple Polynomial Zeros

General Local Convergence Theorems about the Picard Iteration in Arbitrary Normed Fields with Applications to Super–Halley Method for Multiple Polynomial Zeros

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 me...

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Bibliographic Details
Main Author: Stoil I. Ivanov
Format: Article
Language:English
Published: MDPI AG 2020-09-01
Series:Mathematics
Subjects:
iterative methods
local convergence
error estimates
normed fields
Super-Halley method
polynomial zeros
Online Access:https://www.mdpi.com/2227-7390/8/9/1599

Internet

https://www.mdpi.com/2227-7390/8/9/1599

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