Generalized inverse eigenvalue problem for matrices whose graph is a path

Sen, Mausumi; Sharma, Debashish

doi:10.1016/j.laa.2013.12.035

Cited by 8 publications

(3 citation statements)

References 13 publications

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“…This introduces a structural constraint on the solution in addition to the spectral constraint. Thus, one may require that both the matrices H and J or one of them to be, for instance, banded or Hermitian or Hamiltonian [12,16] and so on.…”

Section: Introductionmentioning

confidence: 99%

A generalized inverse eigenvalue problem and m-functions

Behera

2021

Linear Algebra and its Applications

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In this manuscript, a generalized inverse eigenvalue problem is considered that involves a linear pencil (zJ [0,n] − H [0,n] ) of (n + 1) by (n + 1) matrices arising in the theory of rational interpolation and biorthogonal rational functions. In addition to the reconstruction of the Hermitian matrix H [0,n] , characterizations of the rational functions that are components of the prescribed eigenvectors are given. A condition concerning the positive-definiteness of J [0,n] which is often an assumption in the direct problem is also isolated. Further, the reconstruction of H [0,n] is viewed through the inverse of the pencil (zJ [0,n] − H [0,n] ) which involves the concept of m-functions.

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Section: Introductionmentioning

confidence: 99%

A generalized inverse eigenvalue problem and m-functions

Behera

2021

Linear Algebra and its Applications

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“…Eigenvalue problems for matrices with prescribed graphs have also been studied in the literature [2,3,10,13,14]. IEPs concerning the reconstruction of special acyclic matrices like path and broom, from given eigen data have been studied in [17,18]. Inverse eigenvalue problems arise in a number of appli-cations such as control theory, pole assignment problems, system identi cation, structural analysis, mass spring vibrations, circuit theory, mechanical system simulation and graph theory [1,9,13,15].…”

Section: Introductionmentioning

confidence: 99%

Inverse eigenvalue problems for acyclic matrices whose graph is a dense centipede

Sharma

Sen

2018

Special Matrices

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Abstract:The reconstruction of a matrix having a pre-de ned structure from given spectral data is known as an inverse eigenvalue problem (IEP). In this paper, we consider two IEPs involving the reconstruction of matrices whose graph is a special type of tree called a centipede. We introduce a special type of centipede called dense centipede. We study two IEPs concerning the reconstruction of matrices whose graph is a dense centipede from given partial eigen data. In order to solve these IEPs, a new system of nomenclature of dense centipedes is developed and a new scheme is adopted for labelling the vertices of a dense centipede as per this nomenclature . Using this scheme of labelling, any matrix of a dense centipede can be represented in a special form which we de ne as a connected arrow matrix. For such a matrix, we derive the recurrence relations among the characteristic polynomials of the leading principal submatrices and use them to solve the above problems. Some numerical results are also provided to illustrate the applicability of the solutions obtained in the paper.

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“…A few special types of inverse eigenvalue problems have been studied in [2][3][4][5][6][7][8]. Inverse problems for matrices with prescribed graphs have been studied in [9][10][11][12][13][14]. Inverse eigenvalue problems arise in a number of applications such as control theory, pole assignment problems, system identification, structural analysis, mass spring vibrations, circuit theory, mechanical system simulation and graph theory [1,12,15,16].…”

Section: Introductionmentioning

confidence: 99%

Inverse Eigenvalue Problems for Two Special Acyclic Matrices

Sharma

Sen

2016

Mathematics

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Abstract:In this paper, we study two inverse eigenvalue problems (IEPs) of constructing two special acyclic matrices. The first problem involves the reconstruction of matrices whose graph is a path, from given information on one eigenvector of the required matrix and one eigenvalue of each of its leading principal submatrices. The second problem involves reconstruction of matrices whose graph is a broom, the eigen data being the maximum and minimum eigenvalues of each of the leading principal submatrices of the required matrix. In order to solve the problems, we use the recurrence relations among leading principal minors and the property of simplicity of the extremal eigenvalues of acyclic matrices.

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Generalized inverse eigenvalue problem for matrices whose graph is a path

Cited by 8 publications

References 13 publications

A generalized inverse eigenvalue problem and m-functions

A generalized inverse eigenvalue problem and m-functions

Inverse eigenvalue problems for acyclic matrices whose graph is a dense centipede

Inverse Eigenvalue Problems for Two Special Acyclic Matrices

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