On a class of higher order methods for simultaneous rootfinding of generalized polynomials

Summary Using the argument principle higher order methods for simultaneous computation of all zeros of generalized polynomials (like algebraic, trigonometric and exponential polynomials or exponential sums) are derived. The methods can also be derived following the continuation principle from 3]. Thereby, the unified approach of 7] is enlarged to arbitrary orderN. The local convergence as well as a-priori and a-posteriori error estimates for these methods are treated on a general level. Numerical examples are included.