Abstract: Predictive type of Chebyshev polynomials are an extension of the Chebyshev polynomials and the best approximation theory, it can solve the general forecast predicted the knowability and controllability problems. Through discussions in the article pointed out, when the prediction error of not more than the known maximum absolute error, predicts will become known; when the prediction interval of not more than the known maximum range, the prediction will be controlled. Based on this principle, the prediction function predictive Chebyshev polynomials, Gn(x) polynomials are established. The polynomials based on differential equations, definitions, properties, mathematical tables, the existence of polynomial problems are demonstrated. The predictive type of the best approximation of g(x) polynomials, at y(x)≠0 conditions by Gn(x) polynomials posed, are provided. A specific algorithm to achieve the g(x) polynomials is presented. A way to make predictions closer to the actual value of the error compensation method is introduced, and some examples are given.

摘要： 预测型切比雪夫多项式，是切比雪夫多项式及最佳逼近理论在预测中的一个推广应用，可以解决一般预测中预测的可知、可控性问题。文中通过讨论后指出，在预测中，当预测误差不超过已知最大绝对误差时，预测将成为可知；当预测区间不超过已知最大范围时，预测将成为可控。基于这个原理，建立了一种具有预测功能的预测型切比雪夫多项式，[Gn(x)]多项式。论证了该多项式依据的微分方程、相关定义、有关性质、数学表式；阐述了该多项式的存在性；给出了[Gn(x)]多项式在[y(x)≠0]条件下构成的预测型最佳逼近[g(x)]多项式；提供了[g(x)]多项式得以实现的具体算法；介绍了一种使预测结果更接近实际值的误差补偿法；并给出了若干应用实例。