Alternative correction equations in the Jacobi-Davidson method

The correction equation in the Jacobi-Davidson method is effective in a subspace orthogonal to the current eigenvector approximation, while for the continuation of the process only vectors orthogonal to the search subspace are of importance. Such a vector is obtained by orthogonalizing the (approximate) solution of the correction equation against the search subspace. As an alternative, a variant of the correction equation can be formulated that is restricted to the subspace orthogonal to the current search subspace. In this paper, we discuss the effectivity of this variant. Our investigation is also motivated by the fact that the restricted correction equation can be used for avoiding stagnation in case of defective eigenvalues. Moreover, this equation plays a key role in the inexact TRQ method cite{SYa98.