Due to the inherent intersymbol interference (ISI), the detection for faster-than-Nyquisy (FTN) signaling is long considered to be a challenging problem. In this paper, we study three equalization and detection schemes in terms of their performance and computational complexity for FTN signaling system. The first one is the widely employed optimal maximum a posterior (MAP) equalization implemented by the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. Although with optimal bit-error-rate (BER) performance, however, it is at the price of greatly increased computational complexity. The following two schemes are mainly based on the linear turbo equalization with much lower complexity. The first one is the frequency domain equalization (FDE) and the second one is the minimum mean-squared error (MMSE) equalization. Computational complexity analysis and numerous simulation results show that even with lower complexity, the linear turbo equalization could asymptotically approach the MAP equalization with negligible BER performance loss, and the MMSE turbo equalization may be a much more suitable detection scheme for future FTN signaling system.