Superfast Iterative Solvers for Linear Matrix Equations

Academician of the RAS E. A. Mikrin^a^,^b^,*, N. E. Zubov^a^,^b, D. E. Efanov^a, and V. N. Ryabchenko^a^,^c
Translated by I. Ruzanova

^aBauman Moscow State Technical University, Moscow, 105005 Russia

^bKorolev Rocket and Space Corporation “Energia,” Korolev, Moscow oblast, 141070 Russia

^cNational Research University “Moscow Power Engineering Institute,” Moscow, 111250 Russia

Correspondence to: *e-mail: mikrin.ea@gmail.com

Received 3 April, 2018

Abstract—Superfast algorithms for solving large systems of linear equations are developed on the basis of an original method for multistep decomposition of a linear multidimensional dynamical system. Examples of analytical synthesis of iterative solvers for matrices of the general form and for large numerical systems of linear algebraic equations are given. For the analytical case, it is shown that convergence occurs at the second iteration.

DOI: 10.1134/S1064562418060145