In order to compensate for hysteresis errors in tracking and manipulation tasks, models describing the piezoceramic actuator nonlinearities are required. These models have to meet the following two criteria: (i) Efficiency and (ii) a bidirectional description of hysteresis phenomena. Due to its flexibility and efficiency, the Preisach operator is a promising tool to model transfer behavior of ferroelectric actuators in forward direction. However, the model cannot be inverted analytically. The scope of this contribution is therefore to introduce a novel, efficient algorithm for the numerical inversion of the Preisach operator. The algorithm is characterized as well as applied to linearize the voltage-deflection hysteresis of trimorph bending actuators. It is shown that independent of the model discretization, a maximum sampling frequency of 6.5 kHz is allowed for the proposed numerical inversion scheme. As result of this fast inversion technique, the Preisach model becomes interesting for real-time hysteresis compensation tasks. It shows to be competitive to other hysteresis models which are directly invertible, such as the Prandtl-Ishlinskii hysteresis operator.