Quadrature based optimal iterative methods

2010/04/16 by Sanjay Kumar Khattri, Khattri, Sanjay K., Ravi P. Agarwal +1
Computer Science · Mathematics · #65H05 #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1004.2930

openalex publication_date 2010/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a simple yet powerful and applicable quadrature based scheme for constructing optimal iterative methods. According to the, still unproved, Kung-Traub conjecture an optimal iterative method based on n+1 evaluations could achieve a maximum convergence order of 2ⁿ. Through quadrature, we develop optimal iterative methods of orders four and eight. The scheme can be further applied to develop iterative methods of even higher order. Computational results demonstrate that the developed methods are efficient as compared with many well known methods.

Citations

• Optimal Order of One-Point and Multipoint Iteration
• Some fourth order multipoint iterative methods for solving equations

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