Research on generalized non‐equidistance GM(1,1) model based on matrix analysis

The purpose of this paper is to establish a new model for non‐equidistance sequence and research affine properties of the new model.

Generalized non‐equidistance GM(1,1) model is put forward based on generalized accumulated generating operation (AGO) theory, and particle swarm optimization is used to solve the parameters of the new model, then affine properties of the new model are researched based on matrix analysis.

The results are convincing: the simulation and prediction precisions of generalized non‐equidistance GM(1,1) model are raised greatly, and it is proved that the affine transformation sequence has the same simulative accuracy with the raw sequence for generalized non‐equidistance GM(1,1) model.

The method exposed in the paper can be used to model and predict for non‐equidistance sequence in the practical problem.

The paper succeeds in establishing a new non‐equidistance grey model and obtaining the affine properties of generalized non‐equidistance GM(1,1) model.