A non-stationary Iterative method for solvrng Ііпеаг system that proposed prevrnusly іб generahzed and researched. So rate of convergence and estimated error formulas of tMs method are derived. An approxrnate rnversrnn algorithm that based on tMs metod was brnlt. It was effective apphes to some dense real matrices whh spedal structure.

1. Balandyn M.Yu., Shuryna E.P. Methods of solving SLA In a large scale. - Novosibirsk: Izd-vo N GTU, 2000. -70 p.
2. Ortega J. Introduction to parallel and vector methods of solving linear systems - M.: Mir, 1991.-356c.
3. L. Hageman, D. Yang. Applied iterative methods. - M.: Mir, 1986. - 446p.
4. Y. Saad. Iterative Methods for Sparse Linear Systems, Second Edition. SIAM /Order Code OT82, 2003. —528 pages.
5. Demmel J. Computational linear algebra. - M.: Mir, 2001. - 429p.
6. I.V. Oseledets and E.E. Tyrtyshnikov. Approximate inversion of matrices in the process of solving a hypersingular integral equation //Comp. Math. and Math. Phys. - 2005. - 45, N2. - P.302-313.

7. V. Olshevsky, I. Oseledets, E. Tyrtyshnikov.Superfast inversion of two-level Toeplitz matrices using Newton iteration and tensor-displacement structure //Operator Theory: Advances and Applications - 2008. - 179, - P.229-240.
8. V. Oseledets, E. E. Tyrtyshnikov and N. L. Zamarashkin. Matrix inversion cases with size-independent tensor rank estimates //Linear Algebra Appl. - 2009. - V. 431, - P.558-570.
9. W. Hackbusch, B.N. Khoromskij and E. Tyrtyshnikov. Approximate iteration for structured matrices //Numer. Math. - 2008., N109. - P.365-383.
10. I. Oseledets. Tensors inside matrices give logarithmic complexity //IM A RAS, Preprint 2009-04 (http://pub.inm.ras.ru); SIAM J. Matrix Anal. Appl. (accepted) - 2009.
11. Abramchuk V.S., Abramchuk I.B. Iterative methods for solving systems Ax = b with optimal acceleration parameters //Dop. N A N Ukrainy. - 1999.- N8. - P.7-12.
12. G. Schulz Iterative Berechnung der reziproken Matrix //Z. angew. Math. und Mech. - 1933.- 13.- N1. - P.57-59.
13. T T Toolbox 1.0 [Electronic resource]: Fast multidimensional array operations in T T format /Oseledets I.V. //-2009. Access mode: http://spring.inm.ras.ru/osel.