ComputationalMathematicsProject

The aim of this project is to propose a solution of the following linear system, taken from the ML Cup by prof. Micheli: $\min_{w} ||\hat{X}w-y||$ where $\hat{X}$ is the matrix obtained by concatenating the (tall thin) matrix from the ML-cup dataset, called $X$, with a few additional columns containing functions of the features of the dataset, and $y$ are the two output columns.

The first algorithm implemented and discussed is the Conjugate Gradient Method, which needs some initial conditions to be met, so the first section will discuss the stage setting. The second part of the report will regard the 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 $Q^T$.