On the fixed-point type Sylvester matrix equations over complete commutative dioids
Behnam Hashemi, Mahtab Mirzaei Khalilabadi, Hanieh Tavakolipour · Electronic Journal of Linear Algebra · 2014
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 ⊗ X ⊕ X ⊗ B ⊕ C. An application is discussed in efficiently solving the minimum cardinality path problem in Cartesian product graphs.