Wavelets linked by differentiation-integration on the unit interval and related applications

Souleymane Kadri Harouna (1) , Valérie Perrier (2)

1 MIA - Mathématiques, Image et Applications - EA 3165
2 CVGI - Calcul des Variations, Géométrie, Image

This paper presents a new construction of biorthogonal multiresolution analyses of L 2 (0, 1) linked by differentiation and integration. The arising wavelets basis is setted to satisfy homogeneous Dirichlet boundary condition, while this requirement is not necessary for the scaling function basis. On this wavelet basis, the solution of Poisson equation is computed by a wavelet coefficients renormalization like in Fourier domain with a linear complexity O(N). Fast algorithms are provided and illustrated by numerical examples.

Mots clés: boundary condition; Poisson equations; wavelet on the interval

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Souleymane Kadri Harouna, Valérie Perrier. Wavelets linked by differentiation-integration on the unit interval and related applications. 2017. ⟨hal-01568431v1⟩