研究了进行流场求解的超快速方法——参数多项式方法的原理。从分析参数多项式方法和加权残值法的联系出发 ,证明得到若取足够多的控制点数 ,无论是控制点数大于基函数个数 ,还是控制点数等于基函数个数 ,或者选取有限个控制点 ,在相应的条件下 ,都可以得出这样的结论 :参数多项式方法的求解结果实质上可等同于加权残值法的求解结果。通过研究 ,进一步认识了参数多项式法原理的完备性 ,为其工程应用提供了理论基础 The principle of parametric polynomial method, an ultra-fast method for solving flow field, is studied. Based on the analysis of the connection between polynomial method and weighted residual method, it is proved that if the number of control points is greater than the number of basis functions, the number of control points is equal to the number of basis functions or a limited number of control points are selected, Under the corresponding conditions, we can draw the conclusion that the solution of the parameter polynomial method can be essentially equivalent to the solution of the weighted residual method. Through the study, we further understand the completeness of the principle of the parameter polynomial method and provide a theoretical basis for its engineering application