J4 ›› 2009, Vol. 27 ›› Issue (05): 476-.
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景文博a,姜会林a,王晓曼b,杨文波b
出版日期:
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作者简介:
基金资助:
国防科工委计划基金资助项目(60677009)
JING Wen-boa,JIANG Hui-lina,WANG Xiao-manb,YANG Wen-bob
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摘要:
为提高双曲线拟合精度和速度,克服M 2因子测量过程中受到随机误差的影响,采用正规方程组拟合双曲线的方法,给出了三角分解法求解正规方程组的快速数值算法。实验结果表明,采用正规方程组求解光束质量M2因子与奇异值分解法所得结果是一致的,且该方法速度快、精度高,运算速度可提高一个数量级。
关键词: M2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.
中图分类号:
景文博,姜会林,王晓曼,杨文波. 正规方程组求解激光束质量M2因子方法的研究[J]. J4, 2009, 27(05): 476-.
JING Wen-bo,JIANG Hui-lin,WANG Xiao-man,YANG Wen-bo. Research on Solving Laser Beam Quality Factor M2 with Normal Equations[J]. J4, 2009, 27(05): 476-.
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http://xuebao.jlu.edu.cn/xxb/CN/Y2009/V27/I05/476
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