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

Author

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

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.

Suggested Citation

  • Chang-Zhou Dong & Hao-Xue Li & Francisco J. Garcia Pacheco, 2022. "Inverse Eigenvalue Problem and Least-Squares Problem for Skew-Hermitian {P,K + 1}-Reflexive Matrices," Journal of Mathematics, Hindawi, vol. 2022, pages 1-9, July.
    • Handle: RePEc:hin:jjmath:2940377
    DOI: 10.1155/2022/2940377
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