In order to solve the problems of speed and accuracy in computing the transmission of light field by the current two kinds of arithmetics, a novel arithmetic of matrix multiplication is proposed. The implementation idea and procedures are given. A simulation example is based on six Gaussian beams coherent combination. The result shows that the speed of fast Fourier transform is perfect, but the calculation is not very accurate. However, the integral arithmetic and the matrix multiplication arithmetic can all get exact far-field intensity distributions. The time costed by these two arithmetics is evenly matched. The former needs 15.7 h and the latter only needs about 2 s. The comparison proves that the matrix multiplication arithmetic has advantages of fast and accuracy, which improves the calculation efficiency considerably.