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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Use of Tensor Formats in Elliptic Eigenvalue Problems
Wolfgang Hackbusch, Boris N. Khoromskij, Stefan A. Sauter and Eugene E. TyrtyshnikovAbstract
We investigate approximations by finite sums of products of functions with separated variables to eigenfunctions of multivariate elliptic operators, and especially conditions providing an exponential decrease of the error with respect to the number of terms. The results of the consistent use of tensor formats can be regarded as a base for a new class of iterative eigensolvers with almost linear complexity in the univariate problem size. The results of numerical experiments clearly indicate the linear-logarithmic scaling of low-rank tensor method in the univariate problem size. The algorithms work equally well for the computation of both, minimal and maximal eigenvalues of the discrete elliptic operators.
- Received:
- 05.11.08
- Published:
- 05.11.08
- MSC Codes:
- 65F30, 65F50, 65N35, 65F10
- Keywords:
- elliptic operators, spectra, eigenfunctions, separable approximations, tensors