An Iterative Approach to the Complex Monge-Amp\`ere Eigenvalue Problem

We present an iterative approach to approximate the solution to the Dirichlet complex Monge-Amp\`ere eigenvalue problem on a bounded strictly pseudoconvex domain in $\C^n$. This approach is inspired by a similar approach initiated by F. Abedin, J. Kitagawa who considered the real Monge-Amp\`ere operator on a strictly convex domain in $\R^N$.