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Gray system theory since the early 1980s, was born, has been widespread concern. It has the required sample data, computing the advantages of convenient, short-term forecast accuracy. But in successively study we found that using accumulation method, least square method on the model parameter estimation, and sometimes GM model there are different degrees of morbid, the rounding of small changes of the data or calculation error is often caused by the predicted value huge error. Therefore, how to overcome the Morbid model, to ensure the reliability and stability of gray prediction has become an important aspect of the improved model. Accumulation method was originally by Italian mathematician PEMarchesi, create a curve-fitting techniques can be used in the GM model parameter estimation. This paper mainly studies the accumulation method GM (1,1) and GM (2,1) GM (0,2) GM (0,3) model of pathological and multiply the transform the cumulative method GM (n h) model Morbid certain. Found that the introduction of GM model parameter estimation after, computational complexity and pathological significantly lower accumulation method, and multiply transformation can further reduce morbid. This paper first introduces the basic principles and existing cumulative accumulation method method GM model, and then the gray model morbidly research progress. GM (1,1) model is the core content of the gray model theory, the the gray gray prediction and gray control is the most widely used model. This paper based on the condition number theory, the accumulation method GM (1,1) model Morbid analysis found that the cumulative method to establish the model is able to handle pathological issues, just a simple multiply transformation of raw data, This transformation does not affect the nature of the high accuracy of the model. GM (2,1) model of two characteristic roots, so the dynamic characteristics reflect monotonous, non-monotonic (ie swing). Accumulation method is introduced to the GM (2,1) model parameter estimation, given a new parameter estimation formulas, found that the calculated amount and condition number than the cumulative method greatly reduced. But there are a larger number of individual, so we the accumulation method GM (2,1) model morbid analysis, the use of multiple transformation can significantly reduce the morbid. Pathological theory study of the gray system model to do some preliminary study, some of the theoretical and methodological innovation results, but there are also many problems, Morbid GM (2,1) model has not been completely resolved, the cumulative The the method GM models condition number is generally smaller theoretical basis remains to be further explored, in the future, we will further research in these areas.
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