## R.A. Cuninghame-Green, K. Zimmermann

*Equation with residuated functions *

Comment.Math.Univ.Carolinae 42,4 (2001) 729-740. **Abstract:**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.

**Keywords:** systems of nonlinear equations, residuation theory, max-algebras

**AMS Subject Classification:** 47J05, 47H05

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