二阶导数的小波多分辨表示与有限差分表示比较

Comparison of the finite difference expression with the multiresolution expression for the second derivation

有限差分法所用的基函数虽然具有紧支撑性,但它的光滑性较差,基于小波基的导数多分辨描述方法,具有很好的局部性和光滑性.本文导出了二阶导数的多分辨表示公式,并与有限差分表示进行了比较分析.

The bases of the finite difference expression for the second derivation has the properties of compactly supported,but less smooth.The multiresolution expression has the properties of compactly support and good smooth,because of supported wavelet bases.In the paper,we proposed the formula of the multiresolution representation for the second derivation,and compared their difference.