The construction of multigrid operators for disordered linear lattice
operators, in particular the fermion matrix in lattice gauge theories, by means
of algebraic multigrid and block LU decomposition is discussed. In this
formalism, the effective coarse-grid operator is obtained as the Schur
complement of the original matrix. An optimal approximation to it is found by a
numerical optimization procedure akin to Monte Carlo renormalization, resulting
in a generalized (gauge-path dependent) stencil that is easily evaluated for a
given disorder field. Applications to preconditioning and relaxation methods
are investigated.Comment: 43 pages, 14 figures, revtex4 styl
