Iterative algorithm of wavelet moments method based on the multi-resolution analysis characteristics of wavelet
Jisong Yang, Lipeng Zhou · 2011
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, restricts the scale of problem to be solved. Although the coefficient matrix formed by the wavelet moments method is sparse, but the traditional algorithm of moments method is still used, not making use of the wavelet's multi-resolution analytical characteristics, the condition number of coefficient matrix is instead higher, the complexity of computation stays at a high level. Based on the wavelet's multi-resolution analytical characteristics, an iterative algorithm of wavelet moments method is introduced, the solution procedure is an iterative process by which the accuracy of solution is increasing step by step based on a less accurate solution. On each step more finer items of wavelet basis function is added and solved only for the coefficient of newly added terms, thus the dimension of coefficient matrix, the condition number and the complexity of computation are all reduced enormously. And it has been confirmed to be effective by a practical computation example.