aprox

A collection of numerical methods for solving equations, solving systems of equations, and performing interpolation. The project includes implementations of well-known numerical methods and is designed as a web application for easy interaction and visualization.

Methods

Solving Equations

• Bisection: A bracketing method that repeatedly bisects an interval and then selects a subinterval in which a root must lie.
• False Position: Similar to the bisection method but uses a linear interpolation to find the root.
• Fixed Point: An iterative method that solves equations by repeatedly applying a function.
• Newton-Raphson: An iterative method that uses the first derivative to find successively better approximations to the roots of a real-valued function.
• Secant: Similar to the Newton-Raphson method but does not require the computation of the derivative.
• Multiple Roots: Methods designed to handle cases where a function has multiple roots.

Solving Systems of Equations

• Jacobi: An iterative algorithm for determining the solutions of a diagonally dominant system of linear equations.
• Gauss-Seidel: An iterative method used to solve a system of linear equations. It is a variant of the Jacobi method.
• SOR (Successive Over-Relaxation): An iterative method that improves the convergence rate of the Gauss-Seidel method.

Interpolation

• Vandermonde: A matrix method for polynomial interpolation.
• Newton: Newton's divided differences interpolation polynomial.
• Lagrange: A method of polynomial interpolation which is simple and straightforward to implement.
• Spline: A method of interpolation where the interpolant is a special type of piecewise polynomial called a spline.

Getting Started

Prerequisites

• Python
• Node.js
• Install required libraries: flask, flask_cors, plotly, osmnx, matplotlib, sympy, scipy, etc.

Installation and usage

To get started with aprox, follow these steps:

1. Clone the repository:

   git clone https://github.com/camilobdez/aprox.git

2. Navigate to the project directory:

   cd aprox/frontend

3. Install the necessary dependencies:

   npm install

4. Navigate to the backend directory and run the application:

   cd aprox/backend
   python app.py

5. Run the application:

   cd aprox/frontend
   npm start

Finally, open your browser and navigate to http://localhost:3000 to interact with the web app.

Demo

application-running.mp4

Acknowledgements

This project was created as part of a numerical analysis course and includes contributions from various open-source libraries.

Collaborators

• Camilo Bermúdez
• Luis Baena