document: Riccati-based preconditioner for computing invariant subspaces of large matrices 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
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