Algorithms for solving the inverse problem associated with KAK=As+1

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摘要

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∈Cn×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.

论文关键词:15A24,15A29,Involutory matrix,{K,s+1}-potent matrix,Spectrum,Algorithm,Inverse problem

论文评审过程:Received 30 November 2015, Revised 21 February 2016, Available online 14 March 2016, Version of Record 29 August 2016.

论文官网地址:https://doi.org/10.1016/j.cam.2016.02.055