Summary: Numerical homogenization tries to approximate solutions of elliptic partial differential equations with strongly oscillating coefficients by the solution of localized problems over small subregions. We develop and analyze a rapidly convergent iterative method for numerical homogenization that shares this feature with existing approaches and is modeled after the Schwarz method. The method is highly parallelizable and of lower computational complexity than comparable methods that as ours do not make explicit or implicit use of a scale separation.