On computational aspects of high-order dual Hahn moments

In this paper, we present two new algorithms for the fast and stable computation of high-order dis-crete orthogonal dual Hahn polynomials (DHPs). These algorithms are essentially based on the proposed computation method of the initial values of DHPs following the order n and the variable s . For both al-gorithms, a single stable value is computed, fully independent of the gamma function that is the source of the numerical overflow, and then the rest of DHPs values are computed recursively via the proposed recurrence scheme. By analyzing the DHPs matrix, we propose a new method, which allows ensuring the numerical stability of high-order DHPs and dual Hahn moments (DHMs) until the last order. This method is based on the use of appropriate stability conditions. The results of simulations and compar-isons carried out show on one hand that the second algorithm with the stability condition allows to compute DHPs up to the order n = 17,603 without propagation of numerical error. On the other hand, the performance of analyzing large-size signals and images by high-order DHMs computed by the pro-posed method significantly exceeds the existing methods in terms of numerical stability, accuracy of re-construction and in terms of maximum size of the analyzed signals and images. After the acceptance of this paper, the proposed algorithms for high-order DHPs computation will be made publically available at https://github.com/AchrafDaoui/On- Computational- Aspects- of- High- Order- Dual- Hahn-Moments .