General convergence theorems for iterative processes and applications to the Weierstrass root-finding method
arXiv:1503.0524352 citationsh-index: 20
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For researchers in numerical analysis and fixed point theory, this provides a more general convergence framework, but the contribution is incremental.
The paper proves general convergence theorems for Picard iteration in cone metric spaces and applies them to analyze the Weierstrass root-finding method, improving and generalizing existing results.
In this paper, we prove some general convergence theorems for the Picard iteration in cone metric spaces over a solid vector space. As an application, we provide a detailed convergence analysis of the Weierstrass iterative method for computing all zeros of a polynomial simultaneously. These results improve and generalize existing ones in the literature.