具有高逼近阶的插值多尺度函数的构造

研究了对应于插值多尺度函数的两尺度矩阵符号的特殊形式，并将其代入逼近阶方程，推导出逼近阶方程的一种新的表达式。给出了构造具有高逼近阶的3尺度紧支撑插值多尺度函数的具体算法，应用该算法设计了几组例子，计算得到了含有一个或两个参数的滤波器的准确表达式，同时计算出了使多尺度函数具有最高正则性的参数值，并画出了相应的光滑的尺度函数图形。

Construction of interpolatory multiscaling functions with high approximation order

We show that the two-scale matrix symbol associated with interpolatory multiscaling functions can be reduced to a special form.Furthermore,a new set of approximation order equations for the multiscaling functions is described in terms of the elements of this special two-scale matrix symbol.An algorithm is provided for constructing compactly supported interpolatory multiscaling functions with dilation factor 3 and higher approximation order.Moreover,the associated families of filters with one-parameter or two-parameters are presented explicitly. The optimal parameter values which allow the multiscaling functions to provide the highest regularity are also computed and the corresponding graphs of the smooth scaling functions are drew.