On the fixed-point type Sylvester matrix equations over complete commutative dioids

Abstract

This paper extends the concept of tropical tensor product defined by Butkovic and Fiedler to general idempotent dioids. Then, it proposes an algorithm in order to solve the fixed-point type Sylvester matrix equations of the form X = A â X â X â B â C. An application is discussed in efficiently solving the minimum cardinality path problem in Cartesian product graphs.