Gaussian elimination is a reliable method for solving linear systems of equations when done by hand, but its reliability comes into question when performed on a computer with finite precision arithmetic. This project aims to get familiar with how finite precision affects Gaussian elimination, observe the effects, and investigate remedies by coding examples in MATLAB. Basic MATLAB coding skills are required.

1.
Can you count on your computer for the Gaussian elimination?
Hamed Zakerzadeh
seyed_hamed.zakerzadeh@math.univ-toulouse.fr
Gaussian elimination is a very simple and effective method for solving linear systems of
equations. It yields the correct solution when it is performed on a piece of paper. But if
you want to do it on your laptop, whose limited memory may consider 1/3 as 0.33333, is it
still reliable? This gives rise to a famous unsolved problem, which if you can solve you may
ask Nick Trefethen (University of Oxford) to pay you $1000 as the reward!
The aim of this project is more humble: to get familiar with the finite precision
arithmetic, to observe how it affects the Gaussian elimination method, and to investigate
and apply some of the existing remedies. Basic coding knowledge, for example in MATLAB,
is needed for this project.