A fast and accurate algorithm is explored for solving two-dimensional electromagnetic scattering from electrically large finite strip arrays on grounded dielectric slabs. The induced current is computed efficiently using the novel spectral algorithm, a recently proposed fast single-level matrix-vector product algorithm that reduces the operation count to O(N), where N is the number of unknowns. This algorithm was originally cast into a forward-backward method, but it can equally be used to accelerate the matrix-vector products on conjugate gradient techniques. Both, transverse magnetic and transverse electric polarizations have been considered. ¿ 2000 American Geophysical Union