When Newman's approximation is used to calculate the low frequency part of the nonlinear transfer between the waves and the forces on an LNG carrier, the CPU time to make the time series reconstruction of wave loads is a small part of the total. However, using full QTF-matrices increases the required work by a factor equal to the number of wave components in the sea states and the total simulation time can be increased by 5 or 10. Moreover, if we consider the multi-directional sea, the double summation becomes a quadruple summation at second order which is extremely time-consuming. There is a way to accelerate this computation by making an algebraic or system approximation of the QTF. The aim of this report is to present the solutions, the problems and the performances of such system approximation. A particular case of approximation consists of factorising the full matrix of QTF, considering only the main (highest modulus) eigenvalues and corresponding eigenvectors. This study will compare the different approaches of this method on a case study furnished by Bureau Veritas. Extensive results are given for QTF uni-directional and some first results are commented for QTF multi-directional.