Added Project and Report

README.md

@@ -2,18 +2,18 @@
 
 Repository for the course Computational Mathematics for Learning and Data Analysis.
 
-# Installation
+## Installation
 These steps are for MacOS, with [```brew```](brew.sh) and ```python3``` already installed.
 
-## Installing Julia
+### Installing Julia
 
 ```sh
 brew install julia
 ```
 
-## Installing JupyterLab and IJulia kernel
+### Installing JupyterLab and IJulia kernel
 
-### IJulia kernel
+#### IJulia kernel
 
 Inside the julia REPL:
 ```julia
@@ -23,7 +23,7 @@ Pkg.add("IJulia")
 
 A simple notebook experience can be obtained by simply running ```noteboot()```, which will install in a separate [```conda```](https://docs.conda.io/en/latest/) environment the needed python packages.
 
-### JupyterLab
+#### JupyterLab
 
 A separate environment with [```virtualenv```](https://pypi.org/project/virtualenv/) or [```virtualenvwrapper```](https://pypi.org/project/virtualenvwrapper/) is recommended.
 
@@ -31,6 +31,39 @@ A separate environment with [```virtualenv```](https://pypi.org/project/virtuale
 pip install jupyterlab
 ```
 
-# Running
+## Running
 
 To run simply start the notebook with ```jupyter lab``` , the julia kernel should be automatically detected.
+
+
+# Project 19 (Non-ML)
+
+## Project
+
+In the folder `Project` there is our implementation for the project.
+
+Project description:
+
+> (P) is the linear least squares problem
+
+> $$\min_{w} \lVert \hat{X}w-\hat{y} \rVert$$
+
+> where
+
+> $$\hat{X}= \begin{bmatrix} X^T \newline \lambda I_m \end{bmatrix},\ \ \hat{y} = \begin{bmatrix} y \newline 0 \end{bmatrix},$$
+
+> with $X$ the (tall thin) matrix from the ML-cup dataset by prof. Micheli, $\lambda > 0$ and $y$ is a random vector.
+
+> - (A1) is an algorithm of the class of **limited-memory quasi-Newton methods**.
+> - (A2) is **thin QR factorization with Householder reflectors**, in the variant where one does not form the matrix $Q$, but stores the Householder vectors $u_k$ and uses them to perform (implicitly) products with $Q$ and $Q^T$.
+
+## Report
+
+In the folder `Report` there is the latex project for the report of the project.
+
+Run to compile:
+```
+pdflatex  -file-line-error -shell-escape  --synctex=1 -interaction=nonstopmode main.tex
+biber main
+pdflatex  -file-line-error -shell-escape  --synctex=1 -interaction=nonstopmode main.tex
+```