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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
2 SISYPHE - SIgnals and SYstems in PHysiology & Engineering
Inria Paris-Rocquencourt
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.
Keywords : control theory iterative methods linear systems matrix algebra
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https://hal.inria.fr/hal-00793584
Contributor : Brigitte Briot <>
Submitted on : Friday, February 22, 2013 - 3:42:24 PM
Last modification on : Monday, October 19, 2020 - 2:34:03 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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