Exploring Fixed Point Theorem in Numerical Analysis: A Comprehensive Python Implementation and Visualization
Year: 2025
Type: article
Abstract: : The use of fixed point theorems in numerical analysis is examined in this work, with an emphasis on how they might be applied to solve optimization and equation problems. Fixed point theorems are essential in many branches of mathematics and engineering because they state that there are points that do not change under specific functions. The paper offers a thorough Python implementation of important fixed point algorithms, emphasizing their useful applications in iterative techniques for solving nonlinear equations. These algorithms include the Banach and Brouwer fixed point theorems. Furthermore, visualizations are created to show how these algorithms perform in terms of convergence and efficacy in various contexts. The goal of the implementation is to give researchers and students in numerical analysis and associated fields an approachable way to comprehend fixed point theorems, as well as theoretical insights and useful tools. The constraints and potential difficulties of applying fixed point approaches in situations involving complicated problem solving are also covered in the study. Keywords- Fixed Point Theorem, Numerical Analysis, Python Implementation, Iterative Methods, Convergence Visualization
Authors: Poonam Maurya, Rita Shukla, Manish Kumar Singh
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6968548648
FWCI:
Cites:
Cited by:
Related to: