基于多分辨率分析特性的小波矩量法迭代算法  

Iterative algorithm of wavelet moments method based on multi-resolution analysis characteristics of wavelet

作　　者：杨继松[1] 周立鹏[1] 韩喆[1] 

机构地区：[1]河南科技大学电子信息工程学院,河南洛阳471003

出　　处：《电源技术》2013年第9期1679-1681,1689,共4页Chinese Journal of Power Sources

摘　　要：鉴于传统的矩量法所生成的系数矩阵稠密,条件数和计算的复杂度都高,限制了矩量法的应用规模。而小波矩量法所生成的系数矩阵虽然稀疏,但由于仍沿用矩量法的传统算法,导致条件数反而更高,计算的规模和复杂度仍居高不下。基于小波的多分辨率分析特性,提出了小波矩量法的迭代算法,变矩量法的一次性整体求解为逐次迭代求解。由于每次求解的仅是新增加的小波基函数项,这样在保留了小波矩量法系数矩阵稀疏性的基础上,又极大地降低了矩阵的求解规模,矩阵的条件数也非常低。从矩阵的稀疏性、矩阵规模和条件数三个方面综合地提高了矩量法的效率,并通过实例计算验证了算法的有效性。In view of the fact that the coefficient matrix produced by the classical moments method is dense, both the condition number and the complexity of computation is high, and restrict the scale of problem to be solved. Although the coefficient matrix produced by the wavelet moments method is sparse, the traditional algorithm of moments method is still used, and the condition number of coefficient matrix and the complexity of computation stays at the high level. Based on the multi-resolution analytical characteristics of wavelet, an iterative algorithm of wavelet moments method was introduced which turned the disposable solution into to an iterative solution gradually. Due to only the new added items of wavelet basis function need to be solved at each time, the scale of the matrix was reduced enormously; the condition number of matrix has been also low under the condition of the matrix remains sparse. The efficiency of moment method was raised comprehensive from the three aspects of the sparse, the scale and the condition number of matrix. And the validity of the iterative algorithm wa confirmed through the computation of example.

关 键 词：矩量法 小波矩量法 迭代算法 小波 

分 类 号：TM153[电气工程—电工理论与新技术]