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
published in: Numerical linear algebra with applications, 19 (2012) 1, p. 133-151
DOI number (of the published article): 10.1002/nla.793
MSC-Numbers: 65F30, 65F50, 65N35, 65F10
Keywords and phrases: elliptic operators, spectra, eigenfunctions, separable approximations, tensors
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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.