Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions

@article{Dolgov2014AlternatingME,
  title={Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions},
  author={S. V. Dolgov and Dmitry V. Savostyanov},
  journal={SIAM J. Scientific Computing},
  year={2014},
  volume={36}
}
In this paper we accomplish the development of the fast rank–adaptive solver for tensor–structured symmetric positive definite linear systems in higher dimensions. In [9] this problem is approached by alternating minimization of the energy function, which we combine with steps of the basis expansion in accordance with the steepest descent algorithm. In this paper we combine the same steps in such a way that the resulted algorithm works with one or two neighboring cores at a time. The recurrent… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 82 references

Adaptive nearoptimal rank tensor approximation for high - dimensional operator equations , Found

  • W. Dahmen
  • Comput . Math .
  • 2014

Tobler , Multilevel Preconditioning and Low Rank Tensor Iteration for Space - Time Simultaneous Discretizations of Parabolic PDEs , Numer

  • R. Andreev, C.
  • 2014

Alternating minimal energy methods for linear systems in higher dimensions

  • S. V. Dolgov, D. V. Savostyanov
  • Part I: SPD systems, arXiv preprint 1301.6068
  • 2013
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