11 October 1994 Finite element multiwavelets
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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 Wi(t), each supported on three intervals. The wavelets are orthogonal to all rescalings Wi(2jt-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.
© (1994) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Vasily Strela, Vasily Strela, Gilbert Strang, Gilbert Strang, } "Finite element multiwavelets", Proc. SPIE 2303, Wavelet Applications in Signal and Image Processing II, (11 October 1994); doi: 10.1117/12.188771; https://doi.org/10.1117/12.188771
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