Superfast iterative solvers for linear matrix equations (Q1709851)

The article offers a new multistep decomposition method for constructing a superfast algorithm for solving a large system of linear equations. The approach used for the analysis of the iterative solvers (on the basis of adaptive control theory methods) is explored and exposed. For the decomposition steps \(S = 1,2,3\), explicit formulas for the matrix \(K\) in the feedback control law \(u_k = Kx_k\) are given. An interesting example for synthesizing a superfast iterative solver is also considered.