# Linear Algebra

## 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 …

## 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 …