Work

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

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13213369

Authors: Hubert Pickmann-Soto, Susana Arela-Pérez, Cristina Manzaneda, Hans Nina

Institutions: University of Tarapacá, Universidad Católica del Norte, Universidad de Antofagasta

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Universidad de Tarapacá