umutazazi / fixed_point_iteration

A program, which will find a root of any function by using Fixed-Point Iteration Method.

Fixed-Point Iteration Root Finder

This repository contains a Python project that implements a web-based application for finding roots of mathematical functions using the fixed-point iteration method. The project is divided into three main components:

Components

1. GUI Application (main.py):

   • A tkinter based graphical user interface allowing users to input a function, an initial guess, tolerance, and maximum iterations.
   • Sends a request to the Flask API to perform the fixed-point iteration.
   • Visualizes the convergence of the iteration process using matplotlib.

2. Flask API (app.py):

   • A Flask web application serving as the backend.
   • Handles POST requests at the /find_root endpoint.
   • Uses the FixedPoint class to compute the root of the function.

3. Fixed-Point Iteration Logic (fixedpoint.py):

   • Contains the FixedPoint class with methods for the fixed-point iteration.
   • fixed_point_iteration: Performs the iteration given a function, initial guess, tolerance, and maximum iterations.
   • find_gx: Finds a suitable function g(x) for the iteration, using symbolic computation.

Getting Started

Prerequisites

• Python 3
• Libraries: flask, numpy, matplotlib, sympy, tkinter, requests

Installation

1. Clone the repository to your local machine.
2. Install the required Python packages:

pip install flask numpy matplotlib sympy requests

Running the Application

1. Start the Flask API:

python app.py

2. Launch the GUI application:

python main.py

Usage

• Enter a function in the GUI's function field (e.g., x**2 - x - 2).
• Set your initial guess, tolerance, and maximum iterations.
• Click "Find Root" to start the computation.
• Observe the convergence process visually in the GUI.

Contributing

Contributions to enhance the functionality or efficiency of this project are welcome. Please follow the standard procedures for contributing to a GitHub project.