Algorithms for solving the inverse problem associated with

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• 作者：Leila Lebtahi^a ; ^{leila.lebtabi@unir.net" class="auth_mail" title="E-mail the corresponding author} ; Ó ; scar Romero^b ; ^{oromero@dcom.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Né ; stor Thome^c ; ^{njthome@mat.upv.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A24 ; 15A29
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：333-341
• 全文大小：428 K

文摘

In previous papers, the authors introduced and characterized a class of matrices called {K,s+1}$\{K,s+1\}$-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$K$ satisfying KA^s+1K=A$K{A}^{s+1}K=A$ for a given matrix A∈C^n×n$A\in {\mathbb{C}}^{n\times n}$ and a given natural number s$s$. The cases s=0$s=0$ and s≥1$s\ge 1$ are separately studied since they produce different situations. In addition, some examples are presented showing the numerical performance of the methods.