This is the fourth post in our series on Krylov subspaces. The previous ones (i.e Arnoldi Iterations and Lanczos Algorithm were mostly focused on eigenvalue and eigenvector computations. In this post we will have a look at solving strategies for linear systems of equations. In particular, we will derive the famous conjugate gradients algorithm.
The conjugate gradients method is one of the most popular solvers for linear systems of equations. There exist countless variations and extensions.