This is a repository containing the implementation of some numerical methods in Python. Methods are lectured in the course MS211 - Cálculo Numérico at Universidade Estadual de Campinas (UNICAMP).
The topics of this course are:
- Floating point arithmetic.
- Real function zeros.
- Linear systems.
- Polynomial interpolation.
- Numerical integration.
- Linear least squares.
- Numerical treatment of ordinary differential equations.
This repository is a subset of the topics lectured in the course. Use carefully and always check the results. This is not an official repository of the course.
This repository contains the implementation of some numerical methods in Python. The methods are divided into the following categories:
- Optimization: Bisection, False Position, Fixed Point Iteration, Newton-Raphson, Secant.
- Matrix: LU Decomposition, QR Decompositon, Gauss-Seidel, Jacobi
- Integration: Riemann Sum, Trapezoidal Rule, Simpson's Rule, Romberg Integration
- ODE: Euler, Heun, Runge-Kutta
Each method is implemented as a function in a separate module. The modules are organized into directories based on the category of the method.
TBD: Add Polynomial Interpolation, Linear Least Squares.
The methods are implemented in the respective directories. To use the methods, you can import the functions from the respective module. For example, to use the bisection method, you can import the bisection function from the optimization module as follows:
from optimization import bisectionYou can then use the bisection function to find the root of a function. For example:
root = bisection(f, a, b, tol)where f is the function, a and b are the initial interval, and tol is the tolerance.
This project is licensed under the MIT License - see the LICENSE file for details.