Geodesic
Equation with residuated functions
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 729-740

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 47H05, 47J05, 90C27, 93C65
Keywords: systems of nonlinear equations; residuation theory; max-algebras 
@article{CMUC_2001__42_4_a12,
     author = {Cuninghame-Green, R. A. and Zimmermann, K.},
     title = {Equation with residuated functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {729--740},
     publisher = {mathdoc},
     volume = {42},
     number = {4},
     year = {2001},
     mrnumber = {1883381},
     zbl = {1068.93039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2001__42_4_a12/}
}
TY  - JOUR
AU  - Cuninghame-Green, R. A.
AU  - Zimmermann, K.
TI  - Equation with residuated functions
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2001
SP  - 729
EP  - 740
VL  - 42
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2001__42_4_a12/
LA  - en
ID  - CMUC_2001__42_4_a12
ER  - 
%0 Journal Article
%A Cuninghame-Green, R. A.
%A Zimmermann, K.
%T Equation with residuated functions
%J Commentationes Mathematicae Universitatis Carolinae
%D 2001
%P 729-740
%V 42
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2001__42_4_a12/
%G en
%F CMUC_2001__42_4_a12
Cuninghame-Green, R. A.; Zimmermann, K. Equation with residuated functions. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 729-740. http://geodesic.mathdoc.fr/item/CMUC_2001__42_4_a12/