Larin, M. P. Using a compensation principle in the algebraic multilevel iteration method for finite element matrices. (English. Russian summary) Zbl 1079.65030 Sib. Zh. Vychisl. Mat. 8, No. 2, 127-142 (2005). An improved version is proposed of the algebraic multilevel iteration method for finite element matrices, which was offered by O. Axelsson and M. Larin [J. Comput. Appl. Math. 89, No. 1, 135–153 (1998; Zbl 0941.65036)]. To speed up the rate of convergence, a family of iterative parameters is used, which are chosen on the base of an error compensation principle. Results of numerical experiments on standard test problems are presented. Reviewer: N. I. Alexandrova (Novosibirsk) MSC: 65F10 Iterative numerical methods for linear systems 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65Y20 Complexity and performance of numerical algorithms 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 65F35 Numerical computation of matrix norms, conditioning, scaling Keywords:algebraic multilevel iteration method; preconditioned conjugate gradient method; finite element; numerical experiments PDF BibTeX XML Cite \textit{M. P. Larin}, Sib. Zh. Vychisl. Mat. 8, No. 2, 127--142 (2005; Zbl 1079.65030)