Control-theoretic design of iterative methods for symmetric linear systems of equations

Amit Bhaya (1) , Pierre-Alexandre Bliman (2) , Fernando Pazos (1)

1 UFRJ - Universidade Federal do Rio de Janeiro [Brasil] = Federal University of Rio de Janeiro [Brazil] = Université fédérale de Rio de Janeiro [Brésil]
2 SISYPHE - SIgnals and SYstems in PHysiology & Engineering

Iterative methods for linear systems with a symmetric positive definite coefficient matrix are designed from a control-theoretic viewpoint. In particular, it is shown that a control-theoretic approach loosely based on m-step dead beat control of the error or residual system, with a suitable definition of error norm can be utilized to design new iterative methods that are competitive with the popular Barzilai-Borwein method, that is well known to be an efficient method with low computational cost. Numerical experiments are reported on to confirm the claimed results.

Mots clés: control theory; iterative methods; linear systems; matrix algebra

Domaines: Informatique [cs]

Amit Bhaya, Pierre-Alexandre Bliman, Fernando Pazos. Control-theoretic design of iterative methods for symmetric linear systems of equations. CDC/CCC 2009 - 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Dec 2009, Shanghai, China. pp.115-120, ⟨10.1109/CDC.2009.5399581⟩. ⟨hal-00793584⟩