scholarly journals An Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Yongxin Yuan
Keyword(s):  
Eigenvalue Problem ◽  
Symmetric Matrix ◽  
Sufficient Conditions ◽  
Positive Semidefinite ◽  
Inverse Eigenvalue Problem ◽  
Stiffness Matrices ◽  
Inverse Eigenvalue ◽  
Second Order Systems ◽  
Necessary And Sufficient ◽  
Semidefinite Matrix

The inverse eigenvalue problem of constructing symmetric positive semidefinite matrix (written as ) and real-valued skew-symmetric matrix (i.e., ) of order for the quadratic pencil , where , are given analytical mass and stiffness matrices, so that has a prescribed subset of eigenvalues and eigenvectors, is considered. Necessary and sufficient conditions under which this quadratic inverse eigenvalue problem is solvable are specified.

Submatrix Constrained Inverse Eigenvalue Problem involving Generalised Centrohermitian Matrices in Vibrating Structural Model Correction

2016 ◽  
Vol 6 (1) ◽  
pp. 42-59 ◽  
Author(s):  
Wei-Ru Xu ◽  
Guo-Liang Chen
Keyword(s):  
Eigenvalue Problem ◽  
Structural Model ◽  
Sufficient Conditions ◽  
Approximation Problem ◽  
Inverse Eigenvalue Problem ◽  
Frobenius Norm ◽  
Structured Matrix ◽  
Inverse Eigenvalue ◽  
Left And Right ◽  
Necessary And Sufficient

AbstractGeneralised centrohermitian and skew-centrohermitian matrices arise in a variety of applications in different fields. Based on the vibrating structure equation where M, D, G, K are given matrices with appropriate sizes and x is a column vector, we design a new vibrating structure mode. This mode can be discretised as the left and right inverse eigenvalue problem of a certain structured matrix. When the structured matrix is generalised centrohermitian, we discuss its left and right inverse eigenvalue problem with a submatrix constraint, and then get necessary and sufficient conditions such that the problem is solvable. A general representation of the solutions is presented, and an analytical expression for the solution of the optimal approximation problem in the Frobenius norm is obtained. Finally, the corresponding algorithm to compute the unique optimal approximate solution is presented, and we provide an illustrative numerical example.

scholarly journals Updating a map of sufficient conditions for the real nonnegative inverse eigenvalue problem

2019 ◽  
Vol 7 (1) ◽  
pp. 246-256 ◽  
Author(s):  
C. Marijuán ◽  
M. Pisonero ◽  
Ricardo L. Soto
Keyword(s):  
Eigenvalue Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Inverse Eigenvalue Problem ◽  
Real Matrix ◽  
Real Numbers ◽  
The Real ◽  
Inclusion Relations ◽  
Inverse Eigenvalue ◽  
Necessary And Sufficient

Abstract The real nonnegative inverse eigenvalue problem (RNIEP) asks for necessary and sufficient conditions in order that a list of real numbers be the spectrum of a nonnegative real matrix. A number of sufficient conditions for the existence of such a matrix are known. The authors gave in [11] a map of sufficient conditions establishing inclusion relations or independency relations between them. Since then new sufficient conditions for the RNIEP have appeared. In this paper we complete and update the map given in [11].

The Inverse Eigenvalue Problem for Symmetric Doubly Arrow Matrices

2013 ◽  
Vol 444-445 ◽  
pp. 625-627
Author(s):  
Kan Ming Wang ◽  
Zhi Bing Liu ◽  
Xu Yun Fei
Keyword(s):  
Eigenvalue Problem ◽  
Special Kind ◽  
Inverse Eigenvalue Problem ◽  
Symmetric Matrices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Real ◽  
Inverse Eigenvalue ◽  
Necessary And Sufficient

In this paper we present a special kind of real symmetric matrices: the real symmetric doubly arrow matrices. That is, matrices which look like two arrow matrices, forward and backward, with heads against each other at the station, . We study a kind of inverse eigenvalue problem and give a necessary and sufficient condition for the existence of such matrices.

An Inverse Eigenvalue Problem for Spring-Mass Systems with Partial Mass Connected to the Ground

2013 ◽  
Vol 353-356 ◽  
pp. 3308-3311
Author(s):  
Xia Tian ◽  
Chuan Xiao Li
Keyword(s):  
Total Mass ◽  
Sufficient Conditions ◽  
Inverse Eigenvalue Problem ◽  
Spring Stiffness ◽  
Positive Mass ◽  
Mass System ◽  
Inverse Eigenvalue ◽  
Physical Elements ◽  
Necessary And Sufficient ◽  
Simply Connected

Consider the simply connected spring-mass system with partial mass connected to the ground. The inverse mode problem of constructing the physical elements of the system from two eigenpairs, the grounding spring stiffness and total mass of the system is considered. The necessary and sufficient conditions for constructing a physical realizable system with positive mass and stiffness elements are established. If these conditions are satisfied, the grounding spring-mass system may be constructed uniquely. The numerical methods and examples are given finally.

scholarly journals A class of constrained inverse eigenvalue problem and associated approximation problem for symmetrizable matrices

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 1903-1909
Author(s):  
Xiangyang Peng ◽  
Wei Liu ◽  
Jinrong Shen
Keyword(s):  
Eigenvalue Problem ◽  
Symmetric Matrix ◽  
Approximation Problem ◽  
Inverse Eigenvalue Problem ◽  
Optimal Approximation ◽  
Original Matrix ◽  
Approximation Solution ◽  
Solvability Conditions ◽  
Inverse Eigenvalue ◽  
Symmetrizable Matrices

The real symmetric matrix is widely applied in various fields, transforming non-symmetric matrix to symmetric matrix becomes very important for solving the problems associated with the original matrix. In this paper, we consider the constrained inverse eigenvalue problem for symmetrizable matrices, and obtain the solvability conditions and the general expression of the solutions. Moreover, we consider the corresponding optimal approximation problem, obtain the explicit expressions of the optimal approximation solution and the minimum norm solution, and give the algorithm and corresponding computational example.

An Inverse Eigenvalue Problem for Star Spring-Mass System

2012 ◽  
Vol 166-169 ◽  
pp. 3348-3351
Author(s):  
Xia Tian ◽  
Chuan Xiao Li
Keyword(s):  
Stiffness Matrix ◽  
Sufficient Conditions ◽  
Inverse Eigenvalue Problem ◽  
Spring Stiffness ◽  
Positive Mass ◽  
Mass System ◽  
Inverse Eigenvalue ◽  
Physical Elements ◽  
Necessary And Sufficient ◽  
Arrowhead Matrix

The mass-normalized stiffness matrix of the star spring-mass system is an arrowhead matrix. Given two eigenpairs of the arrowhead matrix. It is assumed that the total mass of a star spring-mass system is known. The problem of constructing the physical elements of the system from the known data is considered. The necessary and sufficient conditions for the construction of a physical realizable system with positive mass and spring stiffness are established. If these conditions are satisfied, the system may be constructed uniquely.

scholarly journals On the Inverse Eigenvalue Problem for Irreducible Doubly Stochastic Matrices of Small Orders

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Quanbing Zhang ◽  
Changqing Xu ◽  
Shangjun Yang
Keyword(s):  
Eigenvalue Problem ◽  
Matrix Theory ◽  
Stochastic Matrix ◽  
Sufficient Conditions ◽  
Difficult Problem ◽  
Inverse Eigenvalue Problem ◽  
Complex Case ◽  
Real Spectrum ◽  
Complex Spectrum ◽  
Inverse Eigenvalue

The inverse eigenvalue problem is a classical and difficult problem in matrix theory. In the case of real spectrum, we first present some sufficient conditions of a realr-tuple (forr=2; 3; 4; 5) to be realized by a symmetric stochastic matrix. Part of these conditions is also extended to the complex case in the case of complex spectrum where the realization matrix may not necessarily be symmetry. The main approach throughout the paper in our discussion is the specific construction of realization matrices and the recursion when the targetedr-tuple is updated to a(r+1)-tuple.

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