A fully algebraic approach is presented for the evaluation of the non-neighboring group interactions of electromagnetic scattering and radiation problems in the case of the Electric Field Integral Equation (EFIE) method. The proposed method exploits the numerical rank deficiency of the non-neighboring groups interactions in a similar way as the Adaptive Cross Approximation (ACA) method, but following a procedure that leads into considerably lower ranks than ACA. Instead of factorizing the interaction impedance matrix, the proposed method operates on the core of the impedance matrix by factorizing the integral equation kernel (Green's function). The factorization specifically is implemented by following a randomized scheme of selecting rows and columns instead of the time consuming adaptive partial pivoting that ACA does. By these ingredients the proposed Randomized Cross Approximation (RCA) method presents considerably lower ranks than ACA while having a low frequency mathcal{O}(N) and high frequency mathcal{O}(N-{1.75}) complexity for a single non-near interaction.
