关键词: M²因子, 最小二乘法, 正规方程组, 三角分解法

Abstract:

 To improve the precision and speed of fitting hyperbola, and to overcome the influence of random errors between the measurement of laser beam quality factor M ², the method for fitting hyperbola with NE(Normal Equations) is adopted. The fast numerical algorithm of solving the normal equations with triangular decomposition is presented. It is shown by experiments that the M ² factors obtained by the normal equations method is consistent with that solved with SVD(Singular Value Decomposition) method, but the first one is faster and more accurate, the operation speed can be improved by one order of magnitude.