scholarly journals Special singularity function for continuous part of the spectral data in the associated eigenvalue problem for nonlinear equations

2012 ◽  
Vol 53 (6) ◽  
pp. 063504 ◽  
Author(s):  
V. O. Vakhnenko ◽  
E. J. Parkes
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Data ◽  
Nonlinear Equations ◽  
Continuous Part ◽  
Singularity Function ◽  
Special Singularity

scholarly journals Explicit solution for an infinite dimensional generalized inverse eigenvalue problem

2001 ◽  
Vol 26 (9) ◽  
pp. 513-523 ◽  
Author(s):  
Kazem Ghanbari
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Function ◽  
Spectral Data ◽  
Explicit Solution ◽  
Generalized Inverse ◽  
Jacobi Matrix ◽  
Inverse Eigenvalue Problem ◽  
Infinite Dimensional ◽  
Generalized Inverse Eigenvalue Problem ◽  
Inverse Eigenvalue

We study a generalized inverse eigenvalue problem (GIEP),Ax=λBx, in whichAis a semi-infinite Jacobi matrix with positive off-diagonal entriesci>0, andB= diag (b0,b1,…), wherebi≠0fori=0,1,…. We give an explicit solution by establishing an appropriate spectral function with respect to a given set of spectral data.

Topographic waves in open domains. Part 2. Bay modes and resonances

1989 ◽  
Vol 200 ◽  
pp. 77-93 ◽  
Author(s):  
Thomas F. Stocker ◽  
E. R. Johnson
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Eigenvalue Problem ◽  
Cutoff Frequency ◽  
Flat Channel ◽  
Continuous Part ◽  
Depth Profiles ◽  
Countably Infinite ◽  
Infinite Set ◽  
Algebraic Eigenvalue Problem

The topographic wave equation is solved in a domain consisting of a channel with a terminating bay zone. For exponential depth profiles the problem reduces to an algebraic eigenvalue problem. In a flat channel adjacent to a shelf–like bay zone the solutions form a countably infinite set of orthogonal bay modes: the spectrum of eigenfrequencies is purely discrete. A channel with transverse topography allows wave propagation towards and away from the bay: the spectrum has a continuous part below the cutoff frequency of free channel waves. Above this cutoff frequency a finite number (possibly zero) of bay-trapped solutions occur. Bounds for this number are given. At particular frequencies below the cutoff the system is in resonance with the incident wave. These resonances are shown to be associated with bay modes.

scholarly journals Решение обратной задачи для сложного вибронного аналога резонанса Ферми на основе плоских вращений Якоби

2020 ◽  
Vol 128 (11) ◽  
pp. 1614
Author(s):  
В.А. Кузьмицкий
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Data ◽  
Similarity Transformation ◽  
Accurate Solution ◽  
Fermi Resonance ◽  
Matrix Elements ◽  
Second Stage ◽  
The Matrix ◽  
Two Stages ◽  
Orthogonal Similarity Transformation

Based on algebraic methods, we have found an accurate solution for the inverse task for the vibronic analogue of the complex Fermi resonance, i.e. the determination from the spectral data (energies Ek and transition intensities Ik of the observed conglomerate of lines, k = 1, 2, ..., n; n > 2) energies of the «dark» states Am and the matrix elements of their coupling Bm with the «bright» state. The algorithm consists of two stages. At the first stage, the Jacobi plane rotations are used to construct an orthogonal similarity transformation matrix X, for which the elements of the first row obey the requirement (X1k)^2 = Ik, which corresponds to that fact that there is only one non-perturbed «bright» state. At the second stage, the quantities Am and Bm are obtained after solving the eigenvalue problem for block of «dark» states of the matrix Xdiag({Ek})X-1.

Structured inverse eigenvalue problems

Acta Numerica ◽  
2002 ◽  
Vol 11 ◽  
pp. 1-71 ◽  
Author(s):  
Moody T. Chu ◽  
Gene H. Golub
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Data ◽  
Physical System ◽  
Eigenvalue Problems ◽  
Partial Information ◽  
Normal Modes ◽  
Dynamical Behaviour ◽  
Inverse Eigenvalue Problem ◽  
Feasibility Constraints ◽  
Inverse Eigenvalue

An inverse eigenvalue problem concerns the reconstruction of a structured matrix from prescribed spectral data. Such an inverse problem arises in many applications where parameters of a certain physical system are to be determined from the knowledge or expectation of its dynamical behaviour. Spectral information is entailed because the dynamical behaviour is often governed by the underlying natural frequencies and normal modes. Structural stipulation is designated because the physical system is often subject to some feasibility constraints. The spectral data involved may consist of complete or only partial information on eigenvalues or eigenvectors. The structure embodied by the matrices can take many forms. The objective of an inverse eigenvalue problem is to construct a matrix that maintains both the specific structure as well as the given spectral property. In this expository paper the emphasis is to provide an overview of the vast scope of this intriguing problem, treating some of its many applications, its mathematical properties, and a variety of numerical techniques.

Inverse Problem in Vibration for Generating Symmetric Coefficient Matrices

1991 ◽  
Author(s):  
Ladislav Starek ◽  
Daniel J. Inman
Keyword(s):  
Inverse Problem ◽  
Eigenvalue Problem ◽  
Differential Equations ◽  
Spectral Data ◽  
Symmetric Solution ◽  
Second Order ◽  
Inverse Eigenvalue Problem ◽  
Degree Of Freedom ◽  
Mass Damper ◽  
Inverse Eigenvalue

Abstract This paper provides a symmetric solution to the inverse eigenvalue problem for systems defined by second order vector differential equations representing a multiple degree of freedom spring-mass damper system. Formulations are provided for calculating real symmetric coefficient matrices from spectral data. These relations are also defined for both simple and Jordan systems.

Nonlinear Asymmetric Buckling of Truncated Spherical Shells

1970 ◽  
Vol 37 (3) ◽  
pp. 651-660 ◽  
Author(s):  
M. T. Wu ◽  
Shun Cheng
Keyword(s):  
Eigenvalue Problem ◽  
Nonlinear Equations ◽  
Theoretical Study ◽  
Numerical Results ◽  
Equilibrium States ◽  
Geometrical Parameters ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Axisymmetric Equilibrium

This paper is concerned with the theoretical study of buckling of truncated spherical shells. Sander’s nonlinear equations for deep shells are used and the equations of equilibrium are expressed in terms of displacements for spherical shells. Based on these equations, analyses are made for calculating prebuckling axisymmetric equilibrium positions and then examining these equilibrium states for points of bifurcation into asymmetric buckling deformations. An eigenvalue problem is formulated and the buckling loads for truncated spherical shells of different geometrical parameters are obtained numerically. The numerical results for the prebuckling axisymmetric deformations and the points of bifurcation are shown on graphs.

Evolution of spectral data and nonlinear equations

1989 ◽  
Vol 40 (4) ◽  
pp. 459-461 ◽  
Author(s):  
L. A. Sakhnovich
Keyword(s):  
Spectral Data ◽  
Nonlinear Equations
Sign in / Sign up

Export Citation Format

Share Document