多尺度函数时域逼近条件的讨论

Discussion on Approximation Condition of Multi-scaling Functions in Time Domain

根据具有m阶逼近的多尺度函数能够重构所有小于m阶的几何多项式逼近条件,采用数学归纳法,分析了重构方程中的系数之间的性质以及具体的结构,并对这一结构进行推导。以二阶有限元多尺度函数为例,验证了这一方法的正确性。

A multi-scaling function with approximation m can exactly reproduce algebraic polynomials of de-gree<m. On the approximation conditions, the relations of coefficients and the form of coefficients are proved by means of maths induction. By the analysis of an example for finite elements multi-scaling functions, the correctness of the conclusion is proved again.