Tone reservation (TR) has been proposed for peak to average power reduction (PAPR) in real-baseband multicarrier systems [1]. In this technique, the peak reduction signal is computed by optimization via linear programming (LP). As shown in [1], the computational complexity of the LP optimization is largely determined by the complexity of the inverse fast Fourier transform (IFFT) algorithm. In this paper, we use submatrices of the inverse fast Fourier transform (IFFT) to reduce the number of constraints in the LP-based optimization. We show that a significant complexity reduction can be achieved compared to the conventional TR algorithm, with similar PAPR reduction.