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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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