Acceleration of Convergence Speed in FP-Iterative Algorithms via Simulation Models

Naveen Kumar*
Department of Mathematics, University Institute of Sciences (UIS), Chandigarh University, Gharuan, Mohali-140413, Punjab, India
*Corresponding Author: Naveen Kumar, Department of Mathematics, University Institute of Sciences (UIS), Chandigarh University, Gharuan, Mohali-140413, Punjab, India.

Published: May 19, 2025

View Pdf

Abstract  

Fixed point (FP) iterative algorithms are fundamental tools in solving nonlinear equations across various disciplines such as mathematics, computer science, and electrical engineering and other related fields. This paper explores methods to enhance the convergence speed of these algorithms by adjusting their internal parameters, particularly the coefficients involved in iterative schemes. By utilizing simulation models and visual analytics, we demonstrate how such modifications lead to significant improvements in convergence rates. Several numerical examples and graphical illustrations are presented to validate our findings.

Keywords and Phrases: Fixed Point Iteration; Convergence Rate; Nonlinear Equations; Simulation; Banach Space; Contractive Mapping 

.