Inner product computations using periodized daubechies wavelets

Juan Mario Restrepo (1) , Gary Leaf (2)

1 UCLA - University of California [Los Angeles]
2 ANL - Argonne National Laboratory [Lemont]

Inner products of wavelets and their derivatives are presently known as connection coefficients. The numerical calculation of inner products of periodized Daubechies wavelets and their derivatives is reviewed, with the aim at providing potential users of the publicly-available numerical scheme, details of its operation. The numerical scheme for the calculation of connection coefficients is evaluated in the context of approximating differential operators, information which is useful in the solution of partial differential equations using wavelet-Galerkin techniques. Specific details of the periodization of inner products in the solution differential equations are included in this presentation.

Mots clés: connection coefficients; wavelets; Galerkin; differential operators

Domaines: Mathématiques [math]

Juan Mario Restrepo, Gary Leaf. Inner product computations using periodized daubechies wavelets. International Journal for Numerical Methods in Engineering, 1998, 40 (19), ⟨10.1002/(SICI)1097-0207(19971015)40:19<3557::AID-NME227>3.0.CO;2-A⟩. ⟨hal-01323007⟩