Finite element multiwavelets

Vasily Strela; Gilbert Strang

doi:10.1117/12.188771

11 October 1994 Finite element multiwavelets

Vasily Strela, Gilbert Strang

Proceedings Volume 2303, Wavelet Applications in Signal and Image Processing II; (1994) https://doi.org/10.1117/12.188771
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

Finite elements with support on two intervals span the space of piecewise polynomomials with degree 2 n - 1 and n - 1 continuous derivatives. Function values and n - 1 derivatives at each meshpoint determine these `Hermite finite elements'. The n basis functions satisfy a dilation equation with n by n matrix coefficients. Orthogonal to this scaling subspace is a wavelet subspace. It is spanned by the translates of n wavelets W_i(t), each supported on three intervals. The wavelets are orthogonal to all rescalings W_i(2^jt-k), but not to translates at the same level (j equals 0). These new multiwavelets achieve 2 n vanishing moments and high regularity with symmetry and short support.

Citation Download Citation

Vasily Strela and Gilbert Strang "Finite element multiwavelets", Proc. SPIE 2303, Wavelet Applications in Signal and Image Processing II, (11 October 1994); https://doi.org/10.1117/12.188771

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