An Inverse Extremal Eigenproblem for Bordered Tridiagonal Matrices Applied to an Inverse Singular Value Problem for Lefkovitch-Type Matrices

Hubert Pickmann-Soto (), Susana Arela-Pérez, Cristina Manzaneda and Hans Nina
Additional contact information
Hubert Pickmann-Soto: Departamento de Matemática, Facultad de Ciencias, Universidad de Tarapacá, Arica 1000000, Chile
Susana Arela-Pérez: Departamento de Matemática, Facultad de Ciencias, Universidad de Tarapacá, Arica 1000000, Chile
Cristina Manzaneda: Departamento de Matemáticas, Facultad de Ciencias, Universidad Católica del Norte, Antofagasta 1240000, Chile
Hans Nina: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

Mathematics, 2025, vol. 13, issue 21, 1-18

Abstract: This paper focuses on the inverse extremal eigenvalue problem (IEEP) and a special inverse singular value problem (ISVP). First, a bordered tridiagonal matrix is constructed from the extremal eigenvalues of its leading principal submatrices and an eigenvector. Then, based on the previous construction, a Lefkovitch-type matrix is constructed from a particular set of singular values and a singular vector. Sufficient conditions are established for the existence of a symmetric bordered tridiagonal matrix, while the nonsymmetric case is also addressed. Finally, numerical examples illustrating these constructions derived from the main results are presented.

Keywords: inverse eigenvalue problem; inverse singular value problem; interlacinginequalities; bordered tridiagonal matrices; Lefkovitch matrices (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/21/3369/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/21/3369/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:21:p:3369-:d:1777447

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().