Numerical comparison of different algorithms for construction of wavelet matrices

TL;DR

This paper compares two algorithms for constructing wavelet matrices, evaluating their performance through numerical experiments, to determine which method is more efficient and effective for generating wavelet matrix coefficients.

Contribution

It introduces a numerical comparison of two different algorithms for wavelet matrix construction based on recent parametrization methods.

Findings

One algorithm outperforms the other in computational efficiency.

Both algorithms successfully generate wavelet matrices with desired properties.

The comparison provides insights into the practical applicability of each method.

Abstract

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