A New Grey Model Based on Optimizing the Grey Derivative and the Background Value at the Same Time.

Based on both white response and connotation expression are geometric progression in the most primitive grey differential equation of GM(1,1)x(⁰⁾(k)+ax⁽¹⁾(k) = b, this paper begins with generation of the time response function's grey derivative at discrete points. Through derivative's definition, establishing a new GM(1,1) by optimizing grey derivative and background value. Then, getting the best coefficient c by introducing criterion function and it has proved that the new expression has the whitened exponent law coincident property and the whitened coefficient coincident property in theory. Finally, some examples show the new model has higher prediction precision. [ABSTRACT FROM AUTHOR]