Multigrid Incomplete Factorization Methods in Krylov Subspaces

The paper studies multigrid methods for solving systems of linear algebraic equations resulting from the seven-point discretization three-dimensional Dirichlet problem an elliptic differential equation second order in a parallepipedal domain on regular grid. algorithms suggested are presented as special iteration processes incomplete factorization Krylov subspaces with hierarchical recursive vector structure that corresponds to sequence embedded grids and gives rise block tridiagonal representation coefficient matrix original system. convergence iterations is enhanced by using principle compensation row sums also symmetric successive overrelaxation. An arbitrary m-grid method defined recursively, based two-grid method. For simplicity, considered Stieltjes matrices. Issues related generalization larger classes problems and, particular, those unsymmetric matrices discussed.