Filter bank algorithms for piecewise linear prewavelets on arbitrary triangulations

This paper studies algorithms for decomposition, reconstruction, and approximation based on piecewise linear prewavelets on bounded triangulations of arbitrary topology. Our key mathematical result is showing that the Schur complement of the associated two scale matrix is symmetric, positive definite, and well conditioned. Numerical examples suggest that thresholding based on prewavelets yields a smaller approximation error than when based on the simple ‘Faber’ decomposition scheme.