title: Riccati-based preconditioner for computing invariant subspaces of large matrices
abstract: This paper introduces and analyzes the convergence properties of a method that computes an approximation to the invariant subspace associated with a group of eigenvalues of a large not necessarily diagonalizable matrix. The method belongs to the family of projection type methods. At each step, it refines the approximate invariant subspace using a linearized Riccati's equation which turns out to be the block analogue of the correction used in the Jacobi-Davidson method. The analysis conducted in this paper shows that the method converges at a rate quasi-quadratic provided that the approximate invariant subspace is close to the exact one. The implementation of the method based on multigrid techniques is also discussed and numerical experiments are reported
keyphrases: Riccati-based preconditioner invariant subspaces large matrices eigenvalues diagonalizable matrix projection type methods Jacobi-Davidson method multigrid techniques