The Inverse Eigenvalue Problem Of Double Dimensional Jacobi Matrices

The inverse eigenvalue problems for matrices arise in a variety of applications include mathematical physical inverse problem,control design structure analysis and so on.The inverse eigenvalue problems concern the constructions of a matrix with specific structure by using some given eigenvalues or eigenvectors.The eigenvalue of jacobi matrix has a very good isolation propertie,so the inverse eigenvalue problems of jacobi matrices have been widely used in structural mechanics,systems and control,telemetry,signal processing,system simulation and other fields,which has been consid-ered as an important research direction of the interdisciplinary such as computational mathematics and system science.In this paper,we consider two inverse eigenvalue problems as follows:Problem ?.Given a n order jacobi matrix and real numbers ?1<?2<…<?2n,find a Jacobi matrix T2n such that {?i}i=12n are the eigenvalues of T2n,,and Tn is the n order leading principal submatrix of Ten.Problem ?.Given the physical parameters of origin vibration system numbers,increase the capacity of original system,construct a 2n order jacobi matrix S2n with certain conditions.The main contribution is as follows:In the first chapter,we introduce the origin of the matrix inverse problem,the main con-tent of the research,the historical research and development status and the application and research prospects of the inverse problem in modern science and technology.In the second chapter,the inverse eigenvalue problem of double dimension jacobi matrix is discussed.Firstly,we introduced research history addvances in the inverse eigenvalue problem for Double Dimensional Jacobi matrix.Then,we proposed a new algorithm for solving this problem.The Innovation points of the new algorithm are as follows:On one hand,that the new algorithm do not need to reconstruct the n-th leading principal submatrix,on the other hand,it has avioded the calculation of the engenvalue of Tn+1,2n.The numerical examples showed the new method is quite good.In the third chapter,the adjunction of the free vibration system is studied.Firstly,the mechanical model of the vibration system is introduced,and then we discussed how to construct the vibration system satisfies certain conditions from a given system.The solving algorithm and numerical example are given.