A Newton method without evaluation of nonlinear function values

1999/06/09 by W. Chen, Chen, W.
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #G.1.2 #G.1.3 #G.1.5 #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #and Science (cs.CE)

paper · pdf · doi:10.48550/arxiv.cs/9906011

openalex publication_date 1999/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present author recently proposed and proved a relationship theorem between nonlinear polynomial equations and the corresponding Jacobian matrix. By using this theorem, this paper derives a Newton iterative formula without requiring the evaluation of nonlinear function values in the solution of nonlinear polynomial-only problems.

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