The Puiseux Expansions Of Defective Eigenvalue Of Matrix-valued Function

The perturbation of defective eigenvalues of matrix-valued function not only has important theoretical significance, but also has comprehensive applications in many fields, such as dynamic response analysis, model updating, damage detection and structure optimization.This paper mainly studies the Puiseux expansions of defective eigenvalues of analytic matrix-valued function depending on one parameter. Using Newton’s Diagram as a tool, we give the exponents and the coefficients of the higher order term of the Puiseux expansions of defective eigenvalue when the first term of the Puiseux expansions of perturbed eigenvalues are same. Our results are firstly derived under the restriction that the partial multiplicities of defective eigenvalues are equal. Then this restriction is removed and the results in general case are given. Finally, we give some numerical examples to validity our results..