Discrete Multiresolution Analysis Using Hermite Interpolation: Biorthogonal Multiwavelets
Robert F. Warming, Richard M. Beam · SIAM Journal on Scientific Computing · 2000
We generalize Harten's interpolatory multiresolution representation to include Hermite interpolation. Compact Hermite interpolation with optimal order accuracy is used in both the decomposition and reconstruction algorithm. The resulting multiple basis functions (biorthogonal multiwavelets) are symmetric or skew-symmetric, compact, and analytic. Harten's approach has several advantages: the multiresolution scheme is inherently discrete, nonperiodic boundary conditions are easy to implement, and the representation can be extended to nonuniform grids in bounded domains. We demonstrate the compression features of the new multiple basis functions by application to several examples.