单形体体积生长算法（SGA）是一种比较有效的高光谱图像端元提取算法。为了解决多次顺序计算单形体体积所造成的高计算复杂度的问题，基于高维空间单形体体积计算公式实现SGA（NSGA），推导出两种NSGA的快速实现算法：基于矩阵三角分解的NSGA算法（FNSGACF）和基于分块矩阵行列式的NSGA算法（FNSGA）。FNSGACF主要利用改进Cholesky分解方法，将单形体体积的计算转化为矩阵的三角分解，从而降低了计算复杂度，提高了算法的效率。FNSGA引入分块矩阵的思想来简化矩阵行列式的计算，很大程度降低了计算的复杂性。基于仿真实验研究和真实高光谱图像实验研究的结果表明，这两种快速实现算法都在保持NSGA结果的基础上运行更快，达到了快速实现的目的。

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.