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                    -functions and inverse generalized eigenvalue problem

Ghanbari, Kazem

doi:10.1088/0266-5611/17/2/302

Cited by 10 publications

(5 citation statements)

References 6 publications

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“…are derived from the S-matrix which is intimately connected with P N (see equation ( 39)). Note that both sets of the spectral parameters determine a unique (apart from the off-diagonal elements sign) Hamiltonian matrix h of a Jacobi form [8,9]…”

Section: And [7]mentioning

confidence: 99%

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A discrete version of the inverse scattering problem and the J -matrix method

Zaytsev¹

2005

Inverse Problems

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Section: And [7]mentioning

confidence: 99%

“…( 39)]. Notice that the both sets of the spectral parameters determine unique [apart from the off diagonal elements sign] Hamiltonian matrix h of a Jacobi form [8,9]…”

Section: Introductionmentioning

confidence: 99%

A discrete version of the inverse scattering problem and the J -matrix method

Zaytsev¹

2005

Inverse Problems

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“…A few special types of inverse eigenvalue problems for various types of matrices like tridiagonal matrices, Jacobi matrices, arrow matrices, doubly arrow matrices etc. have been studied by several authors ( [4,7,8,16,20]). A useful way of describing the structure of matrices is to represent them by graphs.…”

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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“…Chu in [1] gave a detailed characterization of inverse eigenvalue problems. 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].…”

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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m -functions and inverse generalized eigenvalue problem

Cited by 10 publications

References 6 publications

A discrete version of the inverse scattering problem and the J -matrix method

A discrete version of the inverse scattering problem and the J -matrix method

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

Inverse Eigenvalue Problems for Two Special Acyclic Matrices

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