and

The new generalized Schur pair satisfies

or, since ,

The vectors and can be computed from

Hence, the generalized Schur pair is an eigenpair of the deflated matrix pair

This eigenproblem can be solved again with the Jacobi-Davidson process that we have outlined in §8.4.1. In that process we construct vectors that are orthogonal to and vectors that are orthogonal to . This simplifies the computation of the interaction matrices and , associated with the deflated operators:

and and can be simply computed as and , respectively.