On global convergence of admissibly randomized coordinate descent method

The admissibly randomized coordinate descent method is an effective iteration solver for computing the smallest eigenpairs of symmetric matrices of very large sizes. This randomized iteration method is, however, only proved to be convergent locally. In this work, we are going to demonstrate its global convergence by proving that it always converges to a certain eigenpair of the target matrix for any normalized initial vector. Hence, the convergence theory of this randomized iteration method is further enriched and completed.