Equation with residuated functions
Cuninghame-Green, Ray A. ; Zimmermann, Karel
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 729-740 / Harvested from Czech Digital Mathematics Library
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The structure of solution-sets for the equation $F(x)=G(y)$ is discussed, where $F,G$ are given residuated functions mapping between partially-ordered sets. An algorithm is proposed which produces a solution in the event of finite termination: this solution is maximal relative to initial trial values of $x,y$. Properties are defined which are sufficient for finite termination. The particular case of max-based linear algebra is discussed, with application to the synchronisation problem for discrete-event systems; here, if data are rational, finite termination is assured. Numerical examples are given. For more general residuated real functions, lower semicontinuity is sufficient for convergence to a solution, if one exists.

Publié le : 2001-01-01
Classification:  47H05,  47J05,  90C27,  93C65 
@article{119288,
     author = {Ray A. Cuninghame-Green and Karel Zimmermann},
     title = {Equation with residuated functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {729-740},
     zbl = {1068.93039},
     mrnumber = {1883381},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119288}
}

Cuninghame-Green, Ray A.; Zimmermann, Karel. Equation with residuated functions. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 729-740. http://gdmltest.u-ga.fr/item/119288/

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