拟Shannon区间小波的构造及其在数值逼近中的应用

为克服拟Shannon小波变换边界效应明显，导致计算精度下降的缺点，根据插值小波的概念构造了拟Shannon区间小波，给出了在对连续函数进行数值逼近时，配置点参数j=4，5时的数值计算结果。随着j的增大x=0处的误差越来越突出，且逼近精度越来越高，而边界处的逼近误差并不大，即使j=4时，边界处也没有明显的震荡现象。与拟Shannon小波相比，拟Shannon区间小波不仅精确度更高，而且能有效消除边界效应。

Construction of quasi-Shannon interval wavelet and application in numerical approximation

The quasi Shannon wavelet has explicit boundary effect which results in poor calculation accuracy. A quasi Shannon interval wavelet is constructed based on the concept of interpolation wavelet to overcome that shortcoming. The quasi Shannon wavelet scale function and the quasi Shannon interval wavelet scale function were both used to simulate a continuous function f(x) . The zero continuation method was used in the simulation and the value of collocate point parameter j was specified as 4 and 5. With the increasing of parameter j , the error at x =0 becomes more and more outstanding relative to that at other points, and the numerical precision becomes higher in whole solution domain. It is inspiring that the error is smaller and the Gibbs phenomenon is weaker near the boundary even as j =4. The comparison of the simulation results and corresponding error indicates the quasi Shannon interval wavelet can eliminate the boundary effect effectively and have higher calculation exactness than the quasi Shannon wavelet.