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

Abstract : 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.
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Submitted on : Friday, February 22, 2013 - 3:42:24 PM
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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⟩

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