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ABOX Algebraic Multilevel Iteration AMLI method AMLI preconditioner analysis anisotropies approximation AutoMUG Axelsson balanced semi-coarsening basis functions BBOX Black Box Multigrid block incomplete factorization block pivots boundary conditions boundary value problems Bulgaria coarse grid coefficients computed condition number conjugate gradient method consider constant construction corresponding Davidson algorithm defined denote diagonal blocks diagonal matrix discretization domain dual Schur complement efficient eigenvalue elliptic problems entries equation error estimate fill-in finite element implementation iterative method Krylov subspace methods Lemma linear algebraic linear system M-matrix Math Mathematics MBILU mesh minimal residual method multigrid method multilevel methods multilevel preconditioning multiscale nodes nonsymmetric norm number of iterations numerical results obtained optimal order P.S. Vassilevski parameter PCG method Poisson ratio positive definite preconditioner recursive refinement residual Schur complement Section semi-coarsening AMLI algorithm SIAM smoother solver solving stencil stiffness matrix strengthened C.B.S. inequality symmetric technique Theorem 3.1 triangulation tridiagonal two-level V-cycle vector