Indication of a stability loss in the continuation of invariant subspaces

The stability analysis is considered in the context of the pathfollowing of steady states. The aim is to continue invariant subspaces (IS) of the relevant linearized states such that they would contain all unstable and central modes. The direct predictor–corrector algorithm for continuation of IS (CIS) of a fixed dimension may fail to follow the rightmost modes. The remedy is seen in a combination of CIS with subspace iterations preconditioned by a projected Cayley transform.