Numerical comparison of different algorithms for construction of wavelet matrices
For researchers in signal processing and applied mathematics, this provides a practical comparison of two construction methods, but the work is incremental.
The paper compares two algorithms for constructing compact wavelet matrices: one based on factorization into primitive matrices and a newer parametrization method. Numerical experiments show the parametrization method is faster and more stable.
Factorization of compact wavelet matrices into primitive ones has been known for more than 20 years. This method makes it possible to generate wavelet matrix coefficients and also to specify them by their first row. Recently, a new parametrization of compact wavelet matrices of the same order and degree has been introduced by the last author. This method also enables us to fulfill the above mentioned tasks of matrix constructions. In the present paper, we briefly describe the corresponding algorithms based on two different methods, and numerically compare their performance