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Peer-reviewedCC BY 4.0Mathematics

On a Special Inverse Singular Value Problem for Certain Classes of Hessenberg Matrices

  • Hubert Pickmann-Soto1
  • Hans Nina2
  • Susana Arela-Pérez1
  • Matilde Peña3
  1. 1Departamento de Matemática, Universidad de Tarapacá, Arica 1000000, Chile
  2. 2Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
  3. 3Departamento de Matemática y Estadística, Universidad Católica San Pablo, Arequipa 04001, Peru
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Abstract

This paper addresses an inverse singular value problem for three classes of upper Hessenberg matrices: Leslie-type, companion, and circular bidiagonal matrices. The problem is to construct such matrices from the prescribed extremal singular values of certain submatrices. A connection with known results on inverse extremal eigenvalue problems for bordered diagonal and periodic Jacobi matrices is established. For all matrices, conditions for the existence and uniqueness of solutions are provided, except for the signs of their entries. In the case of Leslie-type and companion matrices, these conditions are necessary and sufficient. For circular bidiagonal matrices, these conditions are only sufficient, and two admissible auxiliary parameters are required. Furthermore, numerical examples illustrate the proposed constructions.

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Cite

BibTeXRIS
BibTeX
@article{pickmannsoto2026special,
  title = {{On a Special Inverse Singular Value Problem for Certain Classes of Hessenberg Matrices}},
  author = {Hubert Pickmann-Soto and Hans Nina and Susana Arela-Pérez and Matilde Peña},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203717},
  url = {https://www.mdpi.com/2227-7390/14/20/3717},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - On a Special Inverse Singular Value Problem for Certain Classes of Hessenberg Matrices
AU  - Hubert Pickmann-Soto
AU  - Hans Nina
AU  - Susana Arela-Pérez
AU  - Matilde Peña
PY  - 2026
DA  - 2026/10/13
JO  - Mathematics
DO  - 10.3390/math14203717
UR  - https://www.mdpi.com/2227-7390/14/20/3717
AB  - This paper addresses an inverse singular value problem for three classes of upper Hessenberg matrices: Leslie-type, companion, and circular bidiagonal matrices. The problem is to construct such matrices from the prescribed extremal singular values of certain submatrices. A connection with known results on inverse extremal eigenvalue problems for bordered diagonal and periodic Jacobi matrices is established. For all matrices, conditions for the existence and uniqueness of solutions are provided, except for the signs of their entries. In the case of Leslie-type and companion matrices, these conditions are necessary and sufficient. For circular bidiagonal matrices, these conditions are only sufficient, and two admissible auxiliary parameters are required. Furthermore, numerical examples illustrate the proposed constructions.
SN  - 2227-7390
ER  -