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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Hubert Pickmann-Soto & Susana Arela-Pérez & Cristina Manzaneda & Hans Nina, 2025. "An Inverse Extremal Eigenproblem for Bordered Tridiagonal Matrices Applied to an Inverse Singular Value Problem for Lefkovitch-Type Matrices," Mathematics, MDPI, vol. 13(21), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:21:p:3369-:d:1777447
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