Studies On Inverse Eigenvalue Problem Of Generalized Centre-symmetric Matrix

The so-called inverse algebraic eigenvalue problem is that under certain restrict conditions against the question: elements of matrix are determined according to eigenvalue or eigenvector. The practical inverse alebraic eigenvalue problem arose in phisical chemistry in the study of molecular structures.It arises in various areas of application in a lot of fields,such as dispersed system of physical mathematic, Quantum chemistry, Molecular spectroscopy, Structural Dynamics, Automatic Control, Structural design and modal analysis and so on.Generalized centre-symmetric matrix play a very important role in the fields of vibration system and finite element analysis. In these fields, inverse eigenvalue problem of generalized center-symmetric matrix is the main mathematical modle. For this reason,this paper mainly discusses a kind of special inverse eigenvalue problem of generalized center-symmetric matrix and its application.This paper first gives the definition, structure, properties of generalized centre -symmetric matrix and its two special types. And the eigenvalue problem of generalized centre-symmetric matrix which is related to Householder matrix is discussed. generalized inverse eigenvalue problem of above special matrix and the problem of the optimal approach with spectrum constraints are solved respectively. At last, according to finite element analysis in the static mechanical problems, the generalized inverse eigenvalue problem on generalized center-symmetric matrix ax = bx(?) has been discussed is used as a mathematical modle to construct algorithm , make numerical computing in Matlab to solve two specific problems in engineering and get solutions.