## Turing Patterns

I’d like here to share the reoprt I prepared for my final project for the course of Numerical Analysis of PDE here at KAUST. All the code to reproduce the image here presented can be found on this dedicated repo. We are interested in solving numerically the PDE system proposed by Alan Turing in 1952 …

## BEM For Helmholtz Sound-Soft Scattering Problem

During the course of Advanced Numerical Methods for PDE we study the Boundary Elements Method (BEM) for the solution of the Sound Soft Scattering Problem, this post is a remake of the report I presented as part of the exam. We fix the notation that we will use from now on in this report, let …

## A case study of the 2019-2020 Lombardy COVID-19 outbreak using a SIR Model.

I will update this blog post when I find time along with data coming from the Outbreak. Code and data can be found in this Github repository. The data used are the one provided by Protezione Civile on the official repository. SIR Model The SIR model is a system of ODEs designed to model the …

## Dahlquist Barrier and Symplectic Integrator For Time-Stepping The Wave Equation

So it’s holiday time and I find some times to write, my objective today would be to present and idea regarding how to use the first and the second Dahlquist barrier theorem to prove some theoretical limit of symplectic integrator. Introduction In this first section we will focus our attention to the numerical method to …

## Conjugated Gradient an Optimal Stopping Time Approach

Introduction Suppose that we have a symmetric matrix and our aim is to solve the linear problem to find the exact solution . One of the algorithm widely implemented to perform such task is the conjugated gradient (CG) method. The standard formulation of the CG method is as follow: We define the initial step: . …

## Arnoldi Iterations

During my first year of undergraduate Maths degree at University of Pavia I was seriously evaluating the possibility to change degree course to something more related to Software Engineering. Thankfully I came across the course of Numerical Linear Algebra, I remember that during that course ideas that I hadn’t fully understood until that moment become …

## Digit Recognition

Recently our student association has organised a Machine Learning Course at Collegio Ghislieri, more  detail can be found here, during this course a variety of  topics were touched. At the end of this course we have organised a competition, which consisted into writing the most accurate Neural Network  (NN) for digit recognition. One of the …

## Recursive use of the Woodbury identity to prove the Neumann series expansion.

While I was playing around with some matrices I had the need to expand the matrix inverse of . While doing so I came across two different tools, one known as the Woodbury identity and the other known as the Neumann series expansion. While messing with the aforementioned results I found out that there is …