共形映射在数据拟合效果评价中的应用  

Application of conformal mapping in effect evaluation of data fitting

作　　者：彭祖武[1] 李小雪[1] 余宏明[1] 

机构地区：[1]中国地质大学工程学院,湖北武汉430074

出　　处：《人民长江》2013年第3期36-39,共4页Yangtze River

摘　　要：数据拟合是一种非常重要的工程数据分析手段,但有时会出现几种拟合方程相关性系数差别很小的情况,难以对拟合方程作出选择。为寻求一种能够对多种数学方程拟合效果进行评价的新方法,利用共形映射以拟合函数方程构造解析函数,通过指数形式,将方程曲线映射成单位圆周,同时也将实测数据点映射到复数坐标系中进行分析评价。研究结论认为,利用共形映射对数据拟合效果进行评价是可行的,其能将很小的数据差异放大,提高数据的分辨率;同时,相比实测数据拟合图件,映射后图件的直观性更强,更有利于对数据拟合效果的分析评价。Data fitting is an effective method for engineering data analysis. However, if the relative coefficients of different fit- ting equations are not distinguished, it is difficult to determine a well fitting equation. In order to seek for a evaluation method that can assess fitting effect of various equations, we use fitting function equation to construct analytic function by conformal map- ping, then the equation curves are mapped into unit circle, and measured data are mapped into a complex coordinate system for analysis and evaluation. The results show that it is feasible to evaluate fitting effect by conformal mapping method that can magni-fy slight differences to increase data resolution. Compared with figures of measured data fitting, the mapped figures are more intu-itive to improve effect evaluation of data fitting.

关 键 词：共形映射 数据拟合 拟合效果 复变函数 

分 类 号：P642[天文地球—工程地质学]