  In this paper, we study randomized and cyclic coordinate descent for convex
unconstrained optimization problems. We improve the known convergence rates in
some cases by using the numerical semidefinite programming performance
estimation method. As a spin-off we provide a method to analyse the worst-case
performance of the Gauss-Seidel iterative method for linear systems where the
coefficient matrix is positive semidefinite with a positive diagonal.
