We present a fast and memory efficient algorithm for the estimation of generalized linear models with an additive separable k-way error component. The brute force approach uses dummy variables to account for the unobserved heterogeneity, but quickly faces computational limits. Thus, we show how a weighted version of the Frisch-Waugh-Lovell theorem combined with the method of alternating projections can be incorporated into a Newton-Raphson algorithm to dramatically reduce the computational costs. The algorithm is especially useful in situations, where generalized linear models with k-way fixed effects based on dummy variables are computationally demanding or even infeasible due to time or memory limitations. In a simulation study and an empirical application we demonstrate the performance of our algorithm.