Inverse Eigenvalue Problem and Least-Squares Problem for Skew-Hermitian {P,K + 1}-Reflexive Matrices

Chang-Zhou Dong, Hao-Xue Li and Francisco J. Garcia Pacheco

Journal of Mathematics, 2022, vol. 2022, 1-9

Abstract: This paper involves related inverse eigenvalue problem and least-squares problem of skew-Hermitian {P,k + 1}-reflexive(antireflexive) matrices and their optimal approximation problems. The above problems are studied by converting them into two simpler cases: k = 1 and k = 2. Firstly, with some special properties of skew-Hermitian {P,k + 1}-reflexive(antireflexive) matrices, the necessary and sufficient conditions for the solvability and the general solution are presented, and the solution of corresponding optimal approximation problems also given, respectively. Then, we give the least-squares solution of AX=B satisfying the special condition by the singular value decomposition. Finally, we give an algorithm and an example to illustrate our results.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:2940377

DOI: 10.1155/2022/2940377

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