A new proof of the cross-rule for the ϵ-algorithm based on Schur-complements

摘要

Matrices of the form H — GE−1 F are called Schur-complements. They are closely related to elimination procedures and to determinantal identities. In this paper, the quotient property for Schur-complements is used to establish the ‘Schur-complement-method’, a useful tool for proving certain formulas. As an example, a new proof of the cross-rule for the ϵ-algorithm is presented.