Stable and effective restarting of the SS--RR and SS--RRR methods for computing partial eigenpairs of Hermitian matrices

We consider stable and effective restarts of the SS--RR and SS--RRR methods for computing the eigenpairs of a large Hermitian matrix $A\in\mathbb{C}^{n\times n}$ with the $n_{ev}$ eigenvalues in a given interval. Taking the CJ--SS--RR and CJ--SS--RRR methods for instance, we prove that the commonly