An inverse eigenvalue problem for Jacobi matrix

Wei, Ying; Dai, Hua

doi:10.1016/j.amc.2014.11.101

Cited by 13 publications

(5 citation statements)

References 8 publications

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“…The performance of various applications is also directly correlated with the spectral features of a grounded Laplacian, which have undergone many studies in recent years as well [9,10]. In this paper, we shed a light on the class of Laplacian matrices associated with path graphs, which have the structure of (asymmetric) Jacobi matrices, and they constitute a class of graphs of great importance which has been widely studied over the years [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

A Distributed Algorithm for the Assignment of the Laplacian Spectrum for Path Graphs

Parlangeli

2023

Mathematics

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In this paper, we bring forward a distributed algorithm for the assignment of a prescribed Laplacian spectrum for path graphs by means of asymmetric weight assignment. We first describe the meaningfulness and the relevance of this mathematical setting in modern technological applications, and some examples are reported, revealing its practical usefulness in a variety of applications. Then, the solution is derived both theoretically and through an algorithm. Special attention is devoted to a distributed implementation of the main algorithm, which is a valuable feature for several modern applications. Finally, the positivity is discussed, which is revealed to be a consequence of the strict interlacing property.

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Section: Introductionmentioning

confidence: 99%

A Distributed Algorithm for the Assignment of the Laplacian Spectrum for Path Graphs

Parlangeli

2023

Mathematics

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“…Therefore so far several constrained and specific inverse eigenvalue problems have been studied [15][16][17][18]. Wei and Dai proposed two numerical algorithms to solve the inverse eigenvalue problem of Jacobi matrix [12]. In [9], the inverse eigenvalue problem and the associated optimal approximation problem for Hermitian reflexive matrices with respect to a normal k + 1-potent matrix were studied considered.…”

Section: Introductionmentioning

confidence: 99%

Matrix LSQR algorithms for solving constrained quadratic inverse eigenvalue problem

Hajarian

2021

Filomat

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The inverse eigenvalue problem appears in many applications such as control design, seismic tomography, exploration and remote sensing, molecular spectroscopy, particle physics, structural analysis, and mechanical system simulation. This paper investigates the matrix form of LSQR methods for solving the quadratic inverse eigenvalue problem with partially bisymmetric matrices under a prescribed submatrix constraint. In order to illustrate the effectiveness and feasibility of our results, one numerical example is presented.

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“…(2005, pp. 15), Wei (2013) and Wei and Dai (2015) for more comprehensive reviews about Jacobi matrices and its IEP.…”

Section: Introductionmentioning

confidence: 99%

Generalized inverse eigenvalue problems for augmented periodic Jacobi Matrices

Sun

2019

Comp. Appl. Math.

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An inverse eigenvalue problem for Jacobi matrix

Cited by 13 publications

References 8 publications

A Distributed Algorithm for the Assignment of the Laplacian Spectrum for Path Graphs

A Distributed Algorithm for the Assignment of the Laplacian Spectrum for Path Graphs

Matrix LSQR algorithms for solving constrained quadratic inverse eigenvalue problem

Generalized inverse eigenvalue problems for augmented periodic Jacobi Matrices

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