Numerical Computing

This repository contains the notebooks I developed during the Numerical Computing course at the University of Bologna.

Notebooks

1. 1_Machine_Precision_and_Basics.ipynb
2. 2_Matrix_and_Linear_Systems.ipynb
3. 3_Singular_Values_Decompositions_and_Image_Compression.ipynb
4. 4_Linear_Least_Squares_Problem_and_Polynomial_Regression.ipynb
5. 5_Solving_Nonlinear_Equations.ipynb
6. 6_Unconstrained_Optimization_and_Gradient_Descent.ipynb
7. 7_Image_Enhancement_Deblurring_and_Denoising.ipynb

Topics covered

1. Linear systems: matrices, norms, LU factorization, Cholesky factorization.
2. Singular value decomposition with applications to image compression.
3. Linear least squares problem and polynomial regression.
4. Nonlinear equations: fixed-point iteration and Newton method.
5. Unconstrained optimization: gradient descent and backtracking line search.
6. Image enhancement: deblurring, denoising, Tikhonov regularization.
7. Super resolution of images and total variation denoising.

Credits

These notebooks are a completed and modified version of the ones created by @sedaboni as exercises for the Numerical Computing course.