Rate-optimal sparse approximation of compact break-of-scale embeddings

Byrenheid, Glenn; Janina, Hübner,; Weimar, Markus

doi:10.1016/j.acha.2023.01.007

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Some Important Wavelet Properties1

Globally Discontinuous Wavelets1

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2024

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Cited by 1 publication

(2 citation statements)

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“…Remark 1 For a smaller range of parameters, this has already been shown in [17], while similar norm equivalences have been derived in [5,29] for wavelets which are at least continuous. Moreover, we should mention that the upper bounds in ( 12) and ( 13) can be extended to − d < s < γ , and −d < t < γ , respectively, whereas the lower bounds can be extended to − γ < s < d, and −γ < t < d, respectively, see e.g.…”

Section: Some Important Wavelet Propertiessupporting

confidence: 61%

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Compression of boundary integral operators discretized by anisotropic wavelet bases

Harbrecht,

von Rickenbach

2024

Numer. Math.

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The present article is devoted to wavelet matrix compression for boundary integral equations when using anisotropic wavelet bases for the discretization. We provide a compression scheme for boundary integral operators of order $$2q$$ 2 q on patchwise smooth and globally Lipschitz continuous mainfolds which amounts to only $$\mathcal {O}(N)$$ O ( N ) relevant matrix coefficients in the system matrix without deteriorating the accuracy offered by the underlying Galerkin scheme. Here, $$N$$ N denotes the degrees of freedom in the related trial spaces. By numerical results we validate our theoretical findings.

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Section: Some Important Wavelet Propertiessupporting

confidence: 61%

“…Furthermore, let u be the solution of (5), and u J the solution of (7). Then, we have the convergence…”

Section: Globally Discontinuous Waveletsmentioning

confidence: 99%