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Wavelet compression of integral operators on sparse tensor spaces: construction, consistency and asymptotically optimal complexity

by N. Reich

(Report number 2008-24)

Abstract
For the Galerkin finite element discretization of integrodifferential equations $B u=f$ on $[0,1]^n$, we present a sparse tensor product wavelet compression scheme. The scheme is of essentially optimal and dimension independent complexity $O(h^{-1}|\log h|^{2(n-1)})$ without corrupting the convergence or smoothness requirements of the original sparse tensor finite element scheme. The operators under consideration are assumed to be of non-negative order and admit a standard kernel $k(\cdot,\cdot)$ (singular only on the diagonal).

Keywords:

@Techreport{R08_388,
  author = {N. Reich},
  title = {Wavelet compression of integral operators on sparse tensor spaces: construction, consistency and asymptotically optimal complexity},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2008-24},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2008/2008-24.pdf },
  year = {2008}
}

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