The Analytic Perturbation Of Defective Eigenvalue

The analytic perturbation of defective eigenvalue has important theoretical significance, and in the field of dynamic optimum design, model updating, structural damage diagnosis, dynamic response analysis has important applications.The thesis mainly studies the analytic perturbation of defective eigenvalue of the nonlinear eigenvalue problem depending on a parameter and the generalized eigenvalue problem depending on a parameter and several parameters. For nonlinear eigenvalue problem depending on a parameter, exponent and coefficient of the second term in the expansion of perturbed eigenvalue are derived when the first term of the expansion of the perturbed eigenvalue are equal. For generalized eigenvalue problem depending on a parameter, the expansion of the defective eigenvalue and the puiseux expansion of the corresponding eigenvector can be obtained; For generalized eigenvalue problem depending on several parameters, we derive the mean of the perturbation eigenvalue and the derivative of the corresponding invariant subspaces.