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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716301145&_mathId=si34.gif&_user=111111111&_pii=S0377042716301145&_rdoc=1&_issn=03770427&md5=9c4cacc79989c59388a451cffd683d7f" title="Click to view the MathML source">{K,s+1}class="mathContainer hidden">class="mathCode">$\{K,s+1\}$-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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716301145&_mathId=si35.gif&_user=111111111&_pii=S0377042716301145&_rdoc=1&_issn=03770427&md5=cc5612a8c9e303a5fbdd47ccf594b9f4" title="Click to view the MathML source">Kclass="mathContainer hidden">class="mathCode">$K$ satisfying class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716301145&_mathId=si36.gif&_user=111111111&_pii=S0377042716301145&_rdoc=1&_issn=03770427&md5=3853bf3d3a7ea4c8889425548288cad9" title="Click to view the MathML source">KA^s+1K=Aclass="mathContainer hidden">class="mathCode">$K{A}^{s+1}K=A$ for a given matrix class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716301145&_mathId=si37.gif&_user=111111111&_pii=S0377042716301145&_rdoc=1&_issn=03770427&md5=bf4ae6e9cc5b796bcacc8430de6774ad" title="Click to view the MathML source">A∈C^n×nclass="mathContainer hidden">class="mathCode">$A\in {\mathbb{C}}^{n\times n}$ and a given natural number class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716301145&_mathId=si38.gif&_user=111111111&_pii=S0377042716301145&_rdoc=1&_issn=03770427&md5=ab938d5b9aec0bd3da22279abc8c7c86" title="Click to view the MathML source">sclass="mathContainer hidden">class="mathCode">$s$. The cases class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716301145&_mathId=si39.gif&_user=111111111&_pii=S0377042716301145&_rdoc=1&_issn=03770427&md5=2966341d4cbb41366c20a2fc733ae6db" title="Click to view the MathML source">s=0class="mathContainer hidden">class="mathCode">$s=0$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716301145&_mathId=si40.gif&_user=111111111&_pii=S0377042716301145&_rdoc=1&_issn=03770427&md5=d6c0e50bbc4ffe7862b1715ff59dbd36" title="Click to view the MathML source">s≥1class="mathContainer hidden">class="mathCode">$s\ge 1$ are separately studied since they produce different situations. In addition, some examples are presented showing the numerical performance of the methods.