Description
In the past, algorithms for solving linear systems of equations have focused on finding a solution that is not only stable with respect to small changes to the input, but with a very small error with respect to the analytical solution. However, this comes at the cost of an increased runtime. There has been an increased need to find a solution to linear system in a small amount of time, requiring modest accuracy. Randomized algorithms are quite beneficial in this aspect in that they can have a smaller runtime than their deterministic counterparts. In this thesis, we explore and then modify Randomized Block Kaczmarz, a randomized algorithm for solving overdetermined linear systems of equations, to see how practically effective it can be.