Filter bank algorithms for piecewise linear prewavelets on arbitrary triangulations (Q1576457)

This paper concerns the practical aspects of using piecewise linear prewavelets over triangulations for decomposition, reconstruction, and approximation via thresholding. The authors show that the Schur complement of the associated two scale matrix is symmetric, positive definite, and well conditioned. This paper is completed with two numerical examples of decomposition, reconstruction, and thresholding both when applying the prewavelet basis and when using the Faber decomposition scheme. In addition the authors compute the condition numbers of the Schur complements for prewavelet decomposition.