[0,1]区间上正交小波基的构造及其数值模拟

[0,1]区间上正交小波基的构造及其数值模拟 THE CONSTRUCTION OF ORTHOGONAL WAVELET BASIS ON [0, 1] AND NUMERICAL SIMULATION 易宝林 Yi Baolin 1 2 first-author 叶碧泉 Ye Biquan 1 2 武汉大学数学系,武汉 武汉大学数学系,武汉 College of Mathematics Science, Wuhan University College of Mathematics Science, Wuhan University ,430072 ,430072 利用具有紧支撑的Daubechies函数构造了有限区间[0，1]上的正交小波基．在此基础上，提出了对一阶微分算子进行数值处理的方法，导出了小波基及其在微分算子作用下对L2[0，1]中的函数的逼近算法，数值计算表明文中提出的算法是稳定且有效的． In this paper, we show the construction of orthogonal wavelet basis on the interval [O,1],using compactly supportted Daubechies, Function. Forwardly, we suggest a kind of method to deal withthe differential operator in view of numerical analysis and derive the appoximation algorithm of wavelet basis and differential operator, which affects on the basis, to functions belonging to LZ [0, fi. Numericalcomputation indicate the stability and effectiveness of the algorithm. 多分辨分析 小波正交基 微分算子 数值模拟 multiresolution analysis wavelet orthogonal basis differential operator numerical simulation O241 国家自然科学基金(61672102) 1998-05-01 2021-04-01 5