Piecewise linear prewavelets over type-2 triangulations

  • JIANSHENG CAOy, DON HONGz
  • Published 2007

Abstract

While the construction of univariate wavelets is well understood (see [1] and [2] for example), however, most of real world applications are multivariate or multiparameter in nature. The construction of multivariate wavelets are much more challenging. In fact, even the case of continuous piecewise linear wavelets construction is unexpectedly complicated, see [7] and references therein. Here, for higher degree splines, we only mention that a hierarchical basis for C cubic bivariate splines over quadrangulations is used for surface compression in [9] very recently. Because of the simplicity in computing with the linear splines, the piecewise linear element becomes one of the most important and useful elements in solving boundary value problems. In the literature on the finite element solutions of differential and integral equations, bases of piecewise linear prewavelets with small support have been constructed in [3–6,11–15]. In [8], a characterization of minimum support piecewise linear prewavelets with 10 non-zero coefficients in the mask is given on

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Cite this paper

@inproceedings{CAOy2007PiecewiseLP, title={Piecewise linear prewavelets over type-2 triangulations}, author={JIANSHENG CAOy and DON HONGz}, year={2007} }