| 趋势面分析中曲面拟合的优化 |
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| 引用本文： | 郭洁冰.趋势面分析中曲面拟合的优化[J].地球科学与环境学报,1992(4). |
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| 作者姓名： | 郭洁冰 |
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| 作者单位： | 西安地质学院物探系 710054 |
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| 摘 要： | 曲面拟合在数学地质中应用广泛。本文讨论用多项式函数对离散点观测值进行曲面拟合的优化过程。采用Gram—Schmidt正交化方法计算实矩阵的Moore-penrose型广义逆矩阵;并给出方程组的最短最小二乘解。优化后的曲面拟合方法降低了中间计算结果中坐标值的方次,因而计算出高阶趋势面系数时精度较高,也可以得到较高的多项式趋势面方程。
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| 关 键 词： | 回归模型 广义逆算法 欧氏范数 最短最小二乘解 拟合度 |
THE CURVED SURFACE QUASI-CONJUNCTION OPTIMIZATION IN THE TREND SURFACE ANALYSIS |
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| Guo Jiebing.THE CURVED SURFACE QUASI-CONJUNCTION OPTIMIZATION IN THE TREND SURFACE ANALYSIS[J].Journal of Earth Sciences and Environment,1992(4). |
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| Authors: | Guo Jiebing |
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| Institution: | Xi 'an College of Geology |
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| Abstract: | The curved surface quasi-conjunction is very widely used in the mathematical geology. This paper discussed the optimal procedure in which the curved surface quasi-conjtnction is made by polynomial function for the surveying value on the discrete points. By using the Gram-Schmidt orthogonalization method, the Moore-penrose type generalized in verse of the practical matrix is calculated and the shortest least squares solution of the system is obtained. The power of coordinate value of intermediate results is decreased in the method. Therefore, the coefficients of the trend surface of high power are to be calculated. The polynomical trend surface equation of higher order may be obtained as well. |
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| Keywords: | Regression model Method of generalized inverse calculation Enclidean norm The thortest least squares solution Estimation of quasi-conjunction |
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