GM(1,1) Grey Model with MATLAB Implementation

The GM(1,1) grey model serves as an effective analytical tool for understanding system uncertainty and mixing properties. The implementation utilizes MATLAB's powerful computational capabilities for efficient matrix operations and differential equation solving. Key algorithmic components include cumulative generation operations (AGO) to reduce data randomness and the construction of grey differential equations using least squares estimation. This compact MATLAB implementation demonstrates core grey modeling techniques through functions like cumsum() for data preprocessing and matrix inversion methods for parameter estimation. The model finds extensive applications across multiple disciplines including economic forecasting, meteorological pattern analysis, and engineering system optimization. By leveraging this model, researchers can extract meaningful patterns from limited data sets, gaining valuable insights into complex system behaviors to support data-driven decision making.