A perturbation result for generalized eigenvalue problems and its application to error estimation in a quadrature method for computing zeros of analytic functions

We consider the quadrature method developed by Kravanja et al. (BIT 39 (4) (1999) 646) for computing all the zeros of an analytic function that lie inside the unit circle. A new perturbation result for generalized eigenvalue problems allows us to obtain a detailed upper bound for the error between the zeros and their approximations. To the best of our knowledge, it is the first time that such an error estimate is presented for any quadrature method for computing zeros of analytic functions. Numerical experiments illustrate our results.