On inversion of some meromorphic matrices

AbstractA problem of inversion of a real symmetric matrix meromorphically depending on a parameter is discussed. Such a matrix arises in a problem of perturbation of a positive semidefinite operator by an operator of finite rank. A number of modal synthesis methods deal with such matrices, referred to as characteristic matrices, in problems of investigating complex conservative systems. It is shown that instead of numerical inversion of the matrix at each given value of the parameter one can calculate the inverse matrix by using an explicit formula similar to that for the matrix itself. To diminish the truncation error in practical calculations, the representation of the inverse matrix via a series with accelerated convergence is obtained