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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Diffusive realizations for solutions of some operator equations: The one-dimensional case
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by Michel Lenczner, Gérard Montseny and Youssef Yakoubi PDF
Math. Comp. 81 (2012), 319-344 Request permission


In this paper we deal with the derivation of state-realizations of linear operators that are solutions to certain operator linear differential equations in one-dimensional bounded domains. We develop two approaches in the framework of diffusive representations: one with complex diffusive symbols; the other with real diffusive symbols. Then, we illustrate the theories and develop numerical methods for a Lyapunov equation arising from optimal control theory of the heat equation. A practical purpose of this approach is real-time computation on a semi-decentralized architecture with low granularity.
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Additional Information
  • Michel Lenczner
  • Affiliation: Femto-St Institute, Time-Frequency 26, Rue de l’Epitaphe, 25030 Besançon, France –and– UTBM, 90010 Belfort Cedex, France
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  • Gérard Montseny
  • Affiliation: LAAS-CNRS 7, avenue du Colonel Roche 31077 Toulouse Cedex 4, France
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  • Youssef Yakoubi
  • Affiliation: UPMC Univ Paris 06, Laboratoire Jacques-Louis Lions, F-75005, Paris Cedex, France
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  • Received by editor(s): September 24, 2009
  • Received by editor(s) in revised form: September 23, 2010
  • Published electronically: July 19, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 319-344
  • MSC (2010): Primary 35-xx, 47A62, 01-08, 47G10
  • DOI:
  • MathSciNet review: 2833497