Investigating the orthogonality conditions of wavelets based on Jacobi polynomials (Q1616277)

The paper analyzes some properties of Jacobi wavelets. These are wavelets constructed using the two-parameter Jacobi polynomials. Mutually orthogonal wavelets are constructed leading to an associated wavelet basis characterized by a minimum Riesz ratio. The discovered wavelets are proved to be good candidates for developing solutions of systems of nonlinear equations based on the Krawczyk operator for finding the roots of the system of nonlinear algebraic equations. The method was already developed by the authors in an earlier work. It consists of an interesting twofold work. It combines both theory and application in wavelets. Recall that wavelet theory itself has become somehow slow compared to faster developments in applications. Hence, the present work may be a good contribution in the field.