ANALISIS KEKONVERGENAN GLOBAL METODE ITERASI CHEBYSHEV

Abstract

This article discusses the analysis of the global convergence of Chebyshev method through the geometric interpretation of how to derive its formula using the parabolic equation. The results of the analysis are posed in the theorems, which state hypotheses criteria when the Chebyshev method converges globally for any initial guess at some intervals. For comparison, the hypotheses criteria when the Euler method and Halley iteration convergen globally are also discussed. In comparing these methods through the computations, we look into the fulfillment of the hypotheses criteria of the theorems for each method and the number of iterations required to obtain the estimated roots.