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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.<\/p>","DOI":"10.1090\/s0025-5718-2011-02485-3","type":"journal-article","created":{"date-parts":[[2011,7,19]],"date-time":"2011-07-19T13:35:55Z","timestamp":1311082555000},"page":"319-344","source":"Crossref","is-referenced-by-count":1,"title":["Diffusive realizations for solutions of some operator equations: The one-dimensional case"],"prefix":"10.1090","volume":"81","author":[{"given":"Michel","family":"Lenczner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G\u00e9rard","family":"Montseny","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Youssef","family":"Yakoubi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2011,7,19]]},"reference":[{"issue":"7","key":"1","doi-asserted-by":"publisher","first-page":"1091","DOI":"10.1109\/TAC.2002.800646","article-title":"Distributed control of spatially invariant systems","volume":"47","author":"Bamieh, Bassam","year":"2002","journal-title":"IEEE Trans. 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