Algorithms for solving the inverse problem associated with KAK = A(s+1)

[EN] In previous papers, the authors introduced and characterized a class of matrices called {K, s+1}-potent. Also, they established a method to construct these matrices. The purpose of this paper is to solve the associated inverse problem. Several algorithms are developed in order to find all involutory matrices K satisfying KAs+1K = A for a given matrix A ¿ C n×n and a given natural number s. The cases s = 0 and s ¿ 1 are separately studied since they produce different situations. In addition, some examples are presented showing the numerical performance of the methods.