函数变换π/2-arctanx的性质研究

THE PROPERTY OF FUNCTION TRANSFORMATION π /2-arctanx

针对反正切函数图像的特点以及函数变换理论和灰色系统建模理论。本文从理论上证明了利用函数π/2-arctanx在对非负递增序列进行变换时,具有缩小信息差异,缩小级比偏差,降低原始数据序列光滑比的特点。通过两组具体数据和实例计算对比验证了此函数变换符合上述性质,从而表明经过此函数变换建立的改进GM(1,1)模型的拟合效果和预测精度均有提高。

Based on the feature of anti- cotangent functional graph,the functional transformation theory and grey system modeling theory. This paper is proved theoretically that the information difference has been decreased,the smooth ratio has been lessen and stepwise ratio deviation has been reduced,when function transformation π /2- arctanx is utilized on non- negative increasing series.The calculated results of two concrete data series and comparison of actual calculation tested this functional transformation could meet above- mentioned properties,indicated that this improved GM( 1,1) model is better both in fitting effectiveness and forecasting accuracy.