Computing Zeros of Analytic Functions via Modiied Moments Based on Formal Orthogonal Polynomials Computing Zeros of Analytic Functions via Modiied Moments Based on Formal Orthogonal Polynomials Computing Zeros of Analytic Functions via Modified Moments Based on Formal Orthogonal Polynomials

We consider the problem of computing all the zeros of an analytic function that lie in the interior of a Jordan curve, together with their respective multiplicities. Our approach uses modiied moments based on formal orthogonal polynomials. Numerical experiments indicate that it is far superior to classical approaches, which consider the usually ill-conditioned map from the Newton sums to the unknowns. Abstract. We consider the problem of computing all the zeros of an analytic function that lie in the interior of a Jordan curve, together with their respective multiplicities. Our approach uses modiied moments based on formal orthogonal polynomials. Numerical experiments indicate that it is far superior to classical approaches, which consider the usually ill-conditioned map from the Newton sums to the unknowns.