A control theory approach to linear equation solvers

We present a new iterative approach for solving linear systems of equations. Our method is inspired by feedback stabilization schemes from robust control and yields a control system, whose parameters can be tuned to achieve prescribed convergence properties. In contrast to well–known iterative solution methods for linear equations from linear algebra, such as GMRES(m) or Arnoldi’s method, the proposed dynamical systems solution algorithms have the advantage of being globally convergent or having tunable convergence properties. Keywords— linear equations, iterative methods, feedback control, stabilization.