Inverse Eigenvalue Problems And Sensitivity Analysis Of Several Special Matrices

Matrix inverse eigenvalue problem has important applications in physics,electrology,solid mechanics and so on,therefore it has always been a hot topic in the field of computational mathematics.At the same time,a sensitivity analysis of eigenvalues of a matrix has an important application in the field of model correction,fault diagnosis and control system structure.So it has the important theoretical significance and practical value.First of all,there have been many achievements in inverse generalized eigenvalue problem.By using factorization of the Hermite generalized inverse Hamilton matrix and singular values decomposition,this paper obtains the general expression of the inverse generalized eigenvalue problem,and gets the optimal approximation solution to a given matrix.Similarly,the generalized inverse eigenvalue problem of anti centrosymmetric and anti-centrosymmetric solutions and the optimal approximation solution is researched.Secondly,in the inverse quadratic eigenvalue problem,this paper analyzes the existing conditions of reflexive solutions,the general expression of the problem and the optimal approximation solution is gived.Then the inverse quadratic eigenvalue problem is transformed into a generalized inverse eigenvalue problem,the solution of the inverse quadratic eigenvalue problem in a class of damped systems is obtained.Finally,in the sensitivity analysis of the eigenvalue of the quadratic matrix polynomial,based on the derivative of the eigenvalue of the generalized eigenvalue problem of regular pencil matrices,this paper obtains the derivative of defective eigenvalues.