Preconditioning constrained eigenvalue problems

The purpose of our paper is to introduce a robust preconditioning scheme for the numerical solution of the leftmost eigenvalues and corresponding eigenvectors of a constrained eigenvalue problem. This constrained eigenvalue problem is congruent to a nonsymmetric eigenvalue problem with nontrivial Jordan blocks associated with infinite eigenvalues. The proposed preconditioning scheme is relevant to the application of Krylov subspace methods and preconditioned eigensolvers. The two key results are a semi-orthogonal decomposition and a transformation process that implicitly combines a preconditioning step followed by abstract projection onto the subspace associated with the finite eigenvalues. Numerical results demonstrate the effectiveness of the preconditioning scheme.