A divide and conquer algorithm on the double dimensional inverse eigenvalue problem for Jacobi matrices

Wu, Xiaoqian

doi:10.1016/j.amc.2012.10.013

Cited by 8 publications

(2 citation statements)

References 16 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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“…The problems are transferred into inverse eigenvalue problems for Jacobi matrices in mathematics. Recently, some new results have been obtained on the inverse eigenvalue problems for Jacobi matrices, see [1][2][3][4]. Using two sets of eigenvalues or two incomplete eigenpairs, the inverse vibration problems of spring-mass systems have been studied by Nylen and Uhlig [5], and Huang, et al [6].…”

Section: Introductionmentioning

confidence: 99%

The Reconstruction of Spring-Mass System with Partial Given Data

Wen-ting¹

2016

Proceedings of the 2015 International Conference on Mechanical Science and Engineering

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In this paper, two inverse vibration problems of constructing a grounding spring-mass system from its two eigenpairs and part of spring stiffness are considered. The vibration system is constrained to satisfy a relation that the total mass of system is a constant, and the problems are transferred into inverse eigenvalue problems for Jacobi matrix. The necessary and sufficient conditions for the construction of physically realizable systems with positive parameters are derived. Furthermore, the corresponding numerical algorithms and numerical example are given.

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An inverse eigenvalue problem for Jacobi matrix

Wei

Dai

2015

Applied Mathematics and Computation

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A divide and conquer algorithm on the double dimensional inverse eigenvalue problem for Jacobi matrices

Cited by 8 publications

References 16 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

The Reconstruction of Spring-Mass System with Partial Given Data

An inverse eigenvalue problem for Jacobi matrix

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