关键词: 正交小波基, 最优化, 随机算法

Abstract: This paper gives several non-linear difference equations based on the orthogonality，regularity and standardity of the orthogonal wavelet with compact support.Then the paper designs a least square objective function from these equations and optimize it by the Gauss-Newton algorithm.However，because of local convergence of Gauss-Newton algorithm，the paper combines the Gauss-Newton algorithm with the stochastic algorithm to get a more feasible algorithm.This algorithm can not only approximate the solutions well given by Daubechies，but also give wavelets which have better symmetricality and locality.Finally，the algorithm proposed can also be used to construct the biorthogonal wavelet or multiwavelet.

Key words: orthonormal wavelet basis, optimization, stochastic algorithm