| Quasi-Regression基函数的选择和算法改进 |
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| 引用本文： | 杨贵军,林路. Quasi-Regression基函数的选择和算法改进[J]. 南开大学学报(自然科学版), 2003, 36(1): 44-49 |
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| 作者姓名： | 杨贵军 林路 |
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| 作者单位： | 南开大学数学科学学院，天津300071 |
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| 基金项目： | 国家自然科学基金资助项目 (1 0 1 71 0 5 1 )，高等学校博士学科点专项科研基金资助项目 (1 9990 0 5 5 1 2 ) |
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| 摘 要： | Quasi—Regression主要用于解决高维空间的函数逼近问题．函数的拟合效果依赖于所选择的标准正交基函数和拟合算法．在很多情况下，未知函数可以表示成若干个部分变量的函数和．本对此提出了一种函数的拟合算法，通过对这些部分变量的函数的拟合，得到原函数的拟合，并且说明新方法精度更高，计算量更少．
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| 关 键 词： | quasi－regression方法 Monte－Carlo 计算机实验 最小二乘估计 正交基函数 函数逼近 |
| 文章编号： | 0465-7942(2003)01-0044-06 |
| 修稿时间： | 2001-06-20 |
SELECTION OF BASIS FUNCTIONS AND IMPROVEMENT OF ALGORITHMS FOR QUASI-REGRESSION |
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| YANG Guijun,LIN Lu. SELECTION OF BASIS FUNCTIONS AND IMPROVEMENT OF ALGORITHMS FOR QUASI-REGRESSION[J]. Acta Scientiarum Naturalium University Nankaiensis, 2003, 36(1): 44-49 |
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| Authors: | YANG Guijun LIN Lu |
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| Abstract: | Quasi-regression was introduced for approximation of a function in high dimensional space in recent literature (reference[2]). The accuracy of approximation to a function depends on the choice of standard orthogonal basis functions and fitting algorithm. In many cases, according to experiences and historical data, it can be deduced that an unknown function is equal to the sum of some other functions each of which only separately includes some of the variables. In this paper an approach for approximating an unknown function from data is given. By approximating these functions respectively, a very good approximation of an unknown function was abtained. It is also verified that the new approach is both more accurate and more computationally efficient than usual ones. |
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| Keywords: | quasi-regresion Monte Carlo computer experiments least square estimate orthogonal basis function |
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