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We propose a low-complexity intercarrier interference/intersymbol interference (ICI/ISI) equalizer for multicarrier transmissions over doubly dispersive channels. Decision-feedback (or interference cancellation) is used with respect to both time and frequency. The ICI stage employs an extension of the iterative LSQR algorithm using groupwise interference cancellation with reliability-based sorting of sets of subcarriers and a band approximation of the frequency-domain channel matrix. The LSQR algorithm is attractive because of its excellent numerical properties and low complexity. Optimal pulse design is optionally considered for shaping the ICI/ISI. Simulation results demonstrate the excellent performance of the proposed ICI/ISI equalizer.