Simplex growing algorithm (SGA) is a kind of effective endmember extraction algorithm for hyperspectral images.In order to solve the high computational complexity problem which arises in the repeating volume calculation for SGA, with SGA that uses hyperspectral spatial simplex volume computation formula (NSGA), two fast implementation algorithms, NSGA algorithm based on matrix factorization (FNSGACF) and NSGA algorithm based on the block matrix determinant (FNSGA), are proposed. FNSGACF uses improved Cholesky decomposition to change simplex volume computation into triangular matrix decomposition, which can reduce the computational complexity and improve the efficiency of the algorithm. FNSGA introduces the idea of partitioned matrix to simplify the computation of the matrix determinant which greatly reduces the computational complexity. The experimental results with the simulated and real hyperspectral data show that these two fast implementation algorithms can perform faster on the basis of keeping results of NSGA and achieve the purpose of fast implementation.