

Preprint 78/2008
Use of Tensor Formats in Elliptic Eigenvalue Problems
Wolfgang Hackbusch, Boris N. Khoromskij, Stefan A. Sauter, and Eugene E. Tyrtyshnikov
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Submission date: 05. Nov. 2008
Pages: 19
published in: Numerical linear algebra with applications, 19 (2012) 1, p. 133-151
DOI number (of the published article): 10.1002/nla.793
Bibtex
MSC-Numbers: 65F30, 65F50, 65N35, 65F10
Keywords and phrases: elliptic operators, spectra, eigenfunctions, separable approximations, tensors
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Abstract:
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.