Iterative optimal arithmetic of weighted average and its application
Shouyu Chen · Journal of Hydraulic Engineering · 2003
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.