Inversion of analytic matrix functions that are singular at the origin

In this paper we study the inversion of an analytic matrix valued function A (z). This problem can also be viewed as an analytic perturbation of the m atrix A(0) = A(0). We are mainly interested in the case where A(0) is singu lar but A (z) has an inverse in some punctured disc around z = 0. It is kno wn that A(-1) (z) can be expanded as a Laurent series at the origin. The ma in purpose of this paper is to provide efficient computational procedures f or the coefficients of this series. We demonstrate that the proposed algori thms are computationally superior to symbolic algebra when the order of the pole is small.