Redundant actuators are introduced in modern aircraft system to increase system flexibility and safety while bring challenges in controller design. Thus, control allocation (CA) methods are used to make control schemes simple. And the adaptive control allocation algorithm can change control parameters according to the current flight condition, which makes it an efficient and robust method. However, in adaptive CA, real-time estimation of matrix means large workload in pseudo-inverse calculation. In order to deal with this problem, this paper proposes two fast solutions for pseudo-inverse computing based on QR and singular value decomposition, and compares their performance in the field of computational speed and accuracy.