摘要
对于小波尺度函数变换的分解系数的积分运算建立了以尺度函数为权的广义高斯积分方法的运算格式．借助于样条函数，证明了其广义高斯积分随小波分解水平（resolutionlevel）指标的上升而收敛．在此基础上给出了以小波尺度函数变换重构或逼近任一函数的显式解析式，并对具有函数算子、微分或积分算子的运算给出了变换规则．这对于求解复杂非线性方程（组）是一种强有力的工具．最后给出了用该文方法求解非线性二点边值问题的算例．
In this paper, a generalized Gaussian integral method is established to take cal-culations of integral for decomposion coefficients of the scaling function transform in the Daubechies wavelet theory. By using the spline functions, it is shown that the generalized Gaussian integral method is convegent as the resolution level increases. After that, an ex-plicit formula of reconstruction of functions based on the scaling function transform is de-duced out. And some expressions are displayed to functional, differential and integral op-erations of functions. It is found that this method is powerful to solve for solutions of strong nonlinear problems. Finally, an example of a two-point boundary-value problem with strong nonlinearity is given to show the efficiency of the method.
出处
《数学物理学报（A辑）》
CSCD
北大核心
1999年第3期293-300,共8页
Acta Mathematica Scientia
基金
国家自然科学基金
国家教委留学回国人员基金
国家教委优秀年轻教师基金
关键词
小波尺度函数
广义高斯积分
误差分析
运算格式
Scaling functions of wavelet, Generalized Gaussian integral, Error estimation, Approximation of functions, applications
