Riesz界与条件数

Riesz Bounds and Conditon Number

在多分辨分析与小波分析中,人们经常要估计Riesz基的上下界.在有限维空间中,这等价于计算Riesz基所对应Gramian矩阵的条件数.本文给出Riesz基与条件数的关系并且讨论了Riesz基加入元素后对Riesz界产生的影响.

People often need to estimate the Riesz bounds in multiresolution analysis and wavelets analysis. In finite condition, this equivalent to compute the condition number of Gramian matrix. This paper gives the relation of Riesz bounds and condition number. Furthermore, we discuss the perturbation of the Riesz bounds when add another elements.