Numerous linear and non-linear data-detection and precoding algorithms for wideband massive multi-user (MU) multiple-input multiple-output (MIMO) wireless systems that rely on orthogonal frequency-division multiplexing (OFDM) or single-carrier frequency-division multiple access (SC-FDMA) require the computation of the Gram matrix for each active subcarrier. Computing the Gram matrix for each active subcarrier, however, results in excessively high computational complexity. In this paper, we propose novel, approximate algorithms that significantly reduce the complexity of Gram-matrix computation by simultaneously exploiting correlation across subcarriers and channel hardening. We show analytically that a small fraction of Gram-matrix computations in combination with approximate interpolation schemes are sufficient to achieve near-optimal error-rate performance at low computational complexity in massive MU-MIMO systems. We also demonstrate that the proposed methods exhibit improved robustness against channel-estimation errors compared to exact Gram-matrix interpolation algorithms that typically require high computational complexity.