Computing connection coefficients of compactly supported wavelets on bounded intervals

C.H. Romine (1) , B.W. Peyton (1)

1 ORNL - Oak Ridge National Laboratory [Oak Ridge]

Daubechies wavelet basis functions have many properties that make them desirable as a basis for a Galerkin approach to solving PDEs: they are orthogonal, with compact support, and their connection coefficients can be computer. The method they developed by Latto et al. to compute connection coefficient dfoes not provide the correct inner product near the endpoints of a bounded interval, making their implementation of boundary conditions problematic. Moreover, the highly oscillatory nature of the wavelet basis functions makes standard numerical quadrature of integrals near the boundary impractical. We extend the method by Latto to construct and solve linear system of equations whose solution provides the exact computation of the integrals at the boundaries. As a consequence, we provide the correct inner product for wavelet basis functions on a bounded interval

Domains: Engineering Sciences [physics]

C.H. Romine, B.W. Peyton. Computing connection coefficients of compactly supported wavelets on bounded intervals. [Research Report] Oak Ridge National Laboratory. 1997. ⟨hal-01321539⟩