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[preprint].pdf

1709.09966.pdf
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🔗 Source: arxiv.org
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👤 Author: LukasExl
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Summary

An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is reformulated as a fitting problem subject to the tangent space without relying on an orthogonality gauge condition. A discrete Euler scheme is established in an alternating least squares framework, where the quadratic subproblems reduce to trace optimization problems that are explicitly solvable using SVD of small size. The method is stable also for larger ranks in the case of small singular values of the core unfoldings and does not require the inverse of matricizations of the core tensor. Regularization of Tikhonov type can be used to compensate for the lack of uniqueness in the tangent space.

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An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low...

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  • File Format: PDF
  • File Size: 893 KB
  • Pages: 18
  • Language: EN
  • Author: LukasExl
  • Total Downloads: 148
  • Last Updated: 2 hours ago

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