| 用奇异值分解求解回归方程的迭代加细 |
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| 引用本文： | 吕纯濂,陈舜华.用奇异值分解求解回归方程的迭代加细[J].南京气象学院学报,1997,20(3):365-369. |
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| 作者姓名： | 吕纯濂 陈舜华 |
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| 作者单位： | [1]南京气象学院基础科学系 [2]南京气象学院大气科学系 |
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| 摘 要： | 在解回归方程时，设计矩阵中的共线性可能产生不精确的参数估计。用奇异值分解的正交矩阵变换可以减少共线性的影响。通过迭代加细过程还可以改进回归系数的估计。本文描述了求解回归方程的奇异值的迭代加细过程。结果表明，在设计矩阵高度共线性时，用奇异值分解的迭代加细可以改进回归系数的估计。
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| 关 键 词： | 回归方程 正交分解 迭代加细 奇异值 分解求解 |
ITERATIVE REFINEMENT OF SVD SOLUTION TO REGRESSION EQUATIONS |
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| Abstract: | In solving the regression equations, collinearity in the design matrix can result in inaccurate parameter estimates. The use of orthogonal matrix transformations such as the singular value decomposition (SVD) can reduce the effect of collinearity. Also, estimates of the regression coefficients can sometimes be improved through iterative refinement. The application of iterative refinement to the SVD solution of the regression equations is described. Results show that iterative refinement using the SVD can improve regression coefficient estimates in the cases where the design matrix is highly collinear. |
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| Keywords: | regression equations collinearity orthogonal decomposition iterative refinement |
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