Novel non-equidistant GM(1,1) model with modified x(t<inf>n</inf>) taken as the initial value for line-drawing data processing

Abstract

Based on the exponential trait of grey model and the definition of integral, the reconstruction method of GM(1,1) model's background value function of nonequal distance sequence was put forward, the approximately expressions of parameters of the background value function were obtained, and a kind of nonequidistant optimum grey model GM(1,1) with modified x(t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) taken as the initial value of response solution to line drawing data processing in computer aided design was proposed, the method of precision inspection was introduced. Then, the programming was implemented with Matlab 7.6 language. An example was given, the results were compared with the results based other grey models, respectively. The method can be used for model establishing on equal interval, as well as on noninterval. Moreover, GM(1,1) model's fitting precision and prediction is advanced and the scope of application is enlarged. The model is simple and practical, and has a generalizing value in the field of CAD.