Constructing pentadiagonal matrices by partial eigen information

Heydari, Mohammad; Fathi, Ferya

doi:10.22061/jdma.2024.11385.1105

Constructing pentadiagonal matrices by partial eigen information

Document Type : Full Length Article

Authors

Mohammad Heydari ¹
Ferya Fathi ²

¹ Department of Computer Science, Khansar Campus, University of Isfahan, Iran.

² Department of Mathematics, Dezful Branch, Islamic Azad University, Dezful, Iran

10.22061/jdma.2024.11385.1105

Abstract

The inverse eigenvalue problem involves constructing a matrix based on its spectral information, along with providing conditions on the input data to determine the solvability of the problem. In this paper, we focus on a specific instance of the inverse eigenvalue problem, known as IEPSP, to generate symmetric pentadiagonal matrices using two pairs of eigenvalues from the desired matrix and an additional eigenvalue from each of its leading principal submatrices. Additionally, we explore a non-negative formulation of the inverse eigenvalue problem to produce a matrix that has non-negative elements. We present sufficient conditions for problem solvability, propose an algorithm, and provide several numerical examples to validate the results.

Graphical Abstract