加权平均的权重优选算法及其应用

通过分析指标值与目标期望值，提出加权平均优选权重的算法。为解除权重的两个约束条件，引入参数，采用e指数函数定义权重。运用最优梯度下降法使目标的计算值与期望值误差最小来迭代优选权重，建立迭代算法模型。将此算法应用于计算龙凤山水库的流域日平均降水量，改进传统计算方法的不足。经过迭代模型对参数率定与检验的误差分析，总误差及每个样本的误差比泰森多边形法的误差明显减小，说明本文提出的算法与应用是科学合理的，便于推广应用。

Iterative optimal arithmetic of weighted average and its application

A weighted average arithmetic for optimizing weights by analyzing criterion values and target expectation values is proposed. A parameter defining the exponential function for calculating weight is introduced to prevent from restrictions. Then, the gradient descending method is applied to optimize the weights by iterative arithmetic to minimize the errors of objective value. The iterative optimal arithmetic is applied to calculate daily average rainfalls in Longfengshan Reservoir drainage basin. The arithmetic combines Thiessen polygon method with isoline method for rainfall and improves the traditional methods greatly. The application demonstrates that the total error is reduced remarkably.