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Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems
We consider linear systems $A(\alpha) x(\alpha) = b(\alpha)$ depending on possibly many parameters $\alpha = (\alpha_1,\ldots,\alpha_p)$. Solving these systems simultaneously for a standardExpand
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Low-rank tensor completion by Riemannian optimization
In tensor completion, the goal is to fill in missing entries of a partially known tensor under a low-rank constraint. We propose a new algorithm that performs Riemannian optimization techniques onExpand
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A literature survey of low‐rank tensor approximation techniques
During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would beExpand
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Algorithm 941: htucker---A Matlab Toolbox for Tensors in Hierarchical Tucker Format
The hierarchical Tucker format is a storage-efficient scheme to approximate and represent tensors of possibly high order. This article presents a Matlab toolbox, along with the underlying methodologyExpand
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A block Newton method for nonlinear eigenvalue problems
  • D. Kressner
  • Computer Science, Mathematics
  • Numerische Mathematik
  • 13 November 2009
We consider matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. One of the most fundamental differences from the linear case is that distinct eigenvalues may have linearlyExpand
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Krylov Subspace Methods for Linear Systems with Tensor Product Structure
The numerical solution of linear systems with certain tensor product structures is considered. Such structures arise, for example, from the finite element discretization of a linear PDE on aExpand
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Parallel algorithms for tensor completion in the CP format
Novel parallel algorithms for tensor completion problems, with applications to recommender systems and function learning.Parallelization strategy offers greatly reduced memory requirements comparedExpand
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Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems
Abstract We consider elliptic PDE eigenvalue problems on a tensorized domain, discretized such that the resulting matrix eigenvalue problem Ax=λx exhibits Kronecker product structure. In particular,Expand
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Learning Heat Diffusion Graphs
Information analysis of data often boils down to properly identifying their hidden structure. In many cases, the data structure can be described by a graph representation that supports signals in theExpand
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Structured Hölder Condition Numbers for Multiple Eigenvalues
The sensitivity of a multiple eigenvalue of a matrix under perturbations can be measured by its Holder condition number. Various extensions of this concept are considered. A meaningful notion ofExpand
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