Mandel and McCormick [2] introduced the RQMG method, which approximately minimizes the Rayleigh quotient over a sequence of grids. In this talk, we will present an algebraic extension. We replace the geometric mesh information with the algebraic information defined by an AMG preconditioner. At each level, we improve the smoother to accelerate the convergence. With a series of numerical experiments, we assess the efficiency of this new algorithm to compute several eigenpairs.

References
[1] T. Chan and I. Sharapov, "Subspace correction multi-level methods for elliptic eigenvalue problems", Numer. Linear Algebra Appl., vol. 9, pp. 1-20 (2002).
[2] J. Mandel and S. McCormick, "A multilevel variational method for Au = λ Bu on composite grids", J. Comput. Phys., vol. 80, pp. 442-452 (1989).