Optimal Control of Iterative Solution Methods for Linear Systems of Equations
Uwe Helmke, Jens Jordan · PAMM · 2005
Abstract Iterative solution methods for linear systems of equations can be regarded as discrete‐time control systems, for which a stabilizing feedback control has to be found. Well known algorithms such as GMRES(m) may exhibit unstable dynamics or sensitive dependence on initial conditions, thus preventing the algorithm to converge to the desired solution. Based on linear system feedback design techniques a new algorithm is proposed that does not suffer under such shortcomings. Global convergence to the desired solution is shown for any initial state. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)