對稱三對角矩陣廣義特征值反問題的若干研究.pdf

1、 IIAbstract AbstractMatrix inverse generalized eigenvalue problem (also called inverse generalized eigenvalueproblem) concerns the reconstruction of matrices under certain constraint conditions which arefrom prescribed

2、complete/partial information of generalized eigenvalues or eigenvectors and frompartial submatrices or elements. The generalized inverse eigenvalue problem is widely involved inrelated fields such as mathematical physics

3、, structural dynamics, molecular optics, etc. With thedevelopment of these fields, many different types of questions have been proposed to promotethe rapid development of the theory of generalized inverse eigenvalue prob

4、lems. However,as the inverse problem cherishes its own complexity, and the theory and the actualdifference, it makes the study of matrix generalized inverse eigenvalue problem process isrelatively slow, except for specia

5、l cases such as symmetric tridiagonal matrix and periodictridiagonal matrix inverse problem research, which mainly use multiple eigenvalues, or the cha-racteristics of the matrix or defect data, or principal submatrices,

6、 to construct the correspondinngmatrix, but the corresponding theoretical results for inverse generalized symmetric tridiagonaleigenvalue problem by the non-principal submatrices and the defected generalizedeigenpairs ar

7、e not common. In this dissertation, two kinds of symmetric tridiagonal matrixinverse generalized eigenvalue problem such as ? ? ? n n C A ? have been considered,Bysplitting the matrix n A into 3 3? block form, when n nn

8、R C ? ? is the diagonal matrix or symm-etric tridiagonal matrices, respectively, the corresponding inverse generalized problem hasbeen studied. This dissertation includes four chapters, which is organized as follows:In C

9、hapter 1, the corresponding background of research and the preliminaryknowledge and the main work of this paper have been illustrated.In Chapter 2, the corresponding basic theory have been introduced.In Chapter 3, We fir

10、st give the definition of the first kind of inverse generalizedeigenvalue problem for symmetric tridiagonal matrix and then the solvable conditionsof this problem and solution form have been presented. Finally, the corre

11、spondingexamples are given.In the end, the definition of the second kind of inverse generalized eigenvalueproblem for symmetric tridiagonal matrix has been proposed and then the solvableconditions of problem and solution