Inverse Eigenvalue Problems for Singular Rank One Perturbations of a Sturm-Liouville Operator

Rank One ◽

Inverse Eigenvalue ◽

This paper is concerned with the inverse eigenvalue problem for singular rank one perturbations of a Sturm-Liouville operator. We determine uniquely the potential function from the spectra of the Sturm-Liouville operator and its rank one perturbations.

Inverse eigenvalue problems for a discontinuous Sturm-Liouville operator with two discontinuities

Boundary Value Problems ◽

10.1186/1687-2770-2013-209 ◽

2013 ◽

Vol 2013 (1) ◽

Cited By ~ 3

Author(s):

Yalçın Güldü

Keyword(s):

Liouville Operator ◽

Eigenvalue Problems ◽

Inverse Eigenvalue ◽

Inverse eigenvalue problem for the discrete three-diagonal Sturm–Liouville operator and the continuum limit

Journal of Physics A General Physics ◽

10.1088/0305-4470/37/39/007 ◽

2004 ◽

Vol 37 (39) ◽

pp. 9139-9155 ◽

Cited By ~ 2

Author(s):

V M Chabanov

Keyword(s):

Eigenvalue Problem ◽

Liouville Operator ◽

Continuum Limit ◽

Inverse Eigenvalue ◽

Sturm Liouville ◽

The Continuum

Inverse eigenvalue problems for a singular Sturm-Liouville operator on (0,1)

Inverse Problems ◽

10.1088/0266-5611/10/4/015 ◽

1994 ◽

Vol 10 (4) ◽

pp. 975-987 ◽

Cited By ~ 25

Author(s):

L A Zhornitskaya ◽

V S Serov

Keyword(s):

Liouville Operator ◽

Eigenvalue Problems ◽

Inverse Eigenvalue ◽

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

Special Matrices ◽

10.1515/spma-2018-0008 ◽

2018 ◽

Vol 6 (1) ◽

pp. 77-92 ◽

Cited By ~ 1

Author(s):

Debashish Sharma ◽

Mausumi Sen

Keyword(s):

Eigenvalue Problem ◽

Recurrence Relations ◽

Eigenvalue Problems ◽

Characteristic Polynomials ◽

Inverse Eigenvalue ◽

Principal Submatrices ◽

Arrow Matrix ◽

New System

Abstract The reconstruction of a matrix having a pre-defined 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 define 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.

On an inverse eigenvalue problem for a semilinear Sturm–Liouville operator

Nonlinear Analysis ◽

10.1016/j.na.2006.11.025 ◽

2008 ◽

Vol 68 (3) ◽

pp. 639-644 ◽

Cited By ~ 3

Author(s):

Peter Zhidkov

Keyword(s):

Eigenvalue Problem ◽

Liouville Operator ◽

Inverse Eigenvalue ◽

An inverse eigenvalue problem for a nonlocal Sturm-Liouville operator

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2020.124661 ◽

2021 ◽

Vol 494 (2) ◽

pp. 124661

Author(s):

Xuewen Wu ◽

Pengcheng Niu ◽

Guangsheng Wei

Keyword(s):

Eigenvalue Problem ◽

Liouville Operator ◽

Inverse Eigenvalue ◽

A CG-Type Method for Inverse Quadratic Eigenvalue Problems in Model Updating of Structural Dynamics

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.09-m0943 ◽

2011 ◽

Vol 3 (1) ◽

pp. 65-86

Author(s):

Jiaofen Li ◽

Xiyan Hu

Keyword(s):

Eigenvalue Problem ◽

Eigenvalue Problems ◽

Model Updating ◽

Computationally Efficient ◽

Type Method ◽

Quadratic Pencil ◽

Model Coefficient ◽

Inverse Eigenvalue ◽

The Difference

AbstractIn this paper we first present a CG-type method for inverse eigenvalue problem of constructing real and symmetric matricesM, DandKfor the quadratic pencilQ(λ) =λ2M+ λD+K, so thatQ(λ) has a prescribed subset of eigenvalues and eigenvectors. This method can determine the solvability of the inverse eigenvalue problem automatically. We then consider the least squares model for updating a quadratic pencilQ(λ). More precisely, we update the model coefficient matrices M, C and K so that (i) the updated model reproduces the measured data, (ii) the symmetry of the original model is preserved, and (iii) the difference between the analytical triplet (M, D, K) and the updated triplet (Mnew,Dnew,Knew) is minimized. In this paper a computationally efficient method is provided for such model updating and numerical examples are given to illustrate the effectiveness of the proposed method.

Inverse Problems in Vibration

Applied Mechanics Reviews ◽

10.1115/1.3149517 ◽

1986 ◽

Vol 39 (7) ◽

pp. 1013-1018 ◽

Cited By ~ 48

Author(s):

Graham M. L. Gladwell

Keyword(s):

Inverse Problems ◽

Eigenvalue Problems ◽

Discrete Systems ◽

Free Vibrations ◽

Continuous Systems ◽

Thin Beam ◽

Elastic Systems ◽

Inverse Eigenvalue ◽

This article concerns infinitesimal free vibrations of undamped elastic systems of finite extent. A review is made of the literature relating to the unique reconstruction of a vibrating system from natural frequency data. The literature is divided into two groups—those papers concerning discrete systems, for which the inverse problems are closely related to matrix inverse eigenvalue problems, and those concerning continuous systems governed either by one or the other of the Sturm–Liouville equations or by the Euler–Bernoulli equation for flexural vibrations of a thin beam.