An Upper Dimension Bound of the Pre-Kernel

The dual representation of the pre-kernel enables us to provide a simple upper dimension bound formula on the pre-kernel set. This upper bound is equal to n − 3, from which we can finally determine a refined assignment on the maximum number of iteration steps required to successfully terminate a pre-kernel search process. At most -iteration steps are needed to single out a member of the pre-kernel under a regime of orthogonal projections.