• TensorToolbox

  • Referenced in 180 articles [sw04185]
  • expressed as the sum of rank-1 tensors. We are interested in the case where...
  • Tensorlab

  • Referenced in 71 articles [sw14255]
  • dense, sparse and incomplete data sets, tensor decompositions: canonical polyadic decomposition (CPD), multilinear singular value ... block term decompositions (BTD) and low multilinear rank approximation (LMLRA), complex optimization: quasi-Newton ... real exact plane search (PS) for tensor optimization, and much ... more: cumulants, tensor visualization, estimating a tensor’s rank or multilinear rank...
  • SDPNAL+

  • Referenced in 53 articles [sw13239]
  • solve large scale SDPs arising from rank-1 tensor approximation problems constructed ... largest rank-1 tensor approximation problem we solved (in about 14.5 h) is nonsym...
  • UQLab

  • Referenced in 41 articles [sw19740]
  • Gaussian process modelling, a.k.a. Kriging, low-rank tensor approximations), rare event estimation (structural reliability), global...
  • LOBPCG

  • Referenced in 33 articles [sw09638]
  • Preconditioned low-rank methods for high-dimensional elliptic PDE eigenvalue problems. We consider elliptic ... eigenvalue problems on a tensorized domain, discretized such that the resulting matrix eigenvalue problem ... solution vector x in a low-rank tensor format. In this paper ... hierarchical Tucker decomposition to develop a low-rank variant of LOBPCG, a classical preconditioned eigenvalue...
  • Package-X

  • Referenced in 13 articles [sw18225]
  • described. Package-X computes arbitrarily high rank tensor integrals with up to three propagators...
  • Cross

  • Referenced in 7 articles [sw30282]
  • Cross: efficient low-rank tensor completion. The completion of tensors, or high-order arrays, attracts ... propose a framework for low-rank tensor completion via a novel tensor measurement scheme that ... show that a third-order tensor of Tucker rank ... error over certain classes of low-rank tensors for the proposed procedure. The results...
  • EFTofPNG

  • Referenced in 7 articles [sw20815]
  • efficiently treating n-point functions as tensors of rank n. The package currently contains four...
  • TKPSVD

  • Referenced in 12 articles [sw28028]
  • tensor, after which a polyadic decomposition with orthogonal rank-1 terms is computed. We prove...
  • ALEA

  • Referenced in 55 articles [sw10167]
  • python framework for spectral methods and low-rank approximations in uncertainty quantification. ALEA is intended ... methods; stochastic Galerkin FEM; adaptive numerical methods; tensor methods for UQ. Most of these areas...
  • TensorBox

  • Referenced in 2 articles [sw35869]
  • decompositions of multiway array data into rank-1 tensors such as CANDECOMP/PARAFAC; Tucker decomposition; Generalized ... Tensor deconvolution; Tensor train decomposition; Best rank-1 tensor approximation; Tensor decomposition with given error...
  • cuTT

  • Referenced in 1 article [sw19961]
  • variety of benchmarks with tensor ranks ranging from 2 to 12 and show that cuTT ... performance is independent of the tensor rank and that it performs no worse than ... scheme for choosing the optimal parameters for tensor transpose algorithms by implementing an analytical...
  • BTTSoftImpute

  • Referenced in 1 article [sw34805]
  • Block tensor train decomposition for missing data estimation. We propose a method for imputation ... matrix data based on a low-rank tensor approximation technique called the block tensor train ... matrices is performed based on a low-rank BTT decomposition, by which storage and time ... scale data matrices admitting a low-rank tensor structure. An iterative soft-thresholding algorithm...
  • t3f

  • Referenced in 4 articles [sw32795]
  • generalization of the low-rank decomposition from matrices to tensors (=multidimensional arrays...
  • E6Tensors

  • Referenced in 1 article [sw22275]
  • Mathematica package E6Tensors, a tool for explicit tensor calculations in gauge theories. In addition ... provides structure constants, various higher rank tensors and expressions for the representations...
  • MUSCO

  • Referenced in 1 article [sw41479]
  • Compression of neural networks. The low-rank tensor approximation is very promising for the compression ... efficient iterative approach, which alternates low-rank factorization with a smart rank selection and fine...
  • TuckerMPI

  • Referenced in 3 articles [sw27856]
  • based on treating the data as a tensor, i.e., a multidimensional array, and computing ... result is a low-rank approximation of the original tensor-structured data. Compression efficiency...
  • PLANC

  • Referenced in 2 articles [sw41123]
  • problem of low-rank approximation of massive dense nonnegative tensor data, for example, to discover ... scalable parallel algorithms to compute the low-rank approximation. We present a software package called ... Parallel Low-rank Approximation with Nonnegativity Constraints, which implements our solution and allows for extension ... data (dense or sparse, matrices or tensors of any order), algorithm (e.g., from multiplicative updating...
  • CoincidentRootLoci

  • Referenced in 3 articles [sw27110]
  • Staglianò - On the algebraic boundaries among typical ranks for real binary forms. It provides some ... useful for working with symmetric tensors of dimension 2. Such tensors are bijectively associated with ... which uses QEPCAD to compute the real rank of binary forms defined over ℚ. This...
  • Deep_Learning

  • Referenced in 3 articles [sw32225]
  • rank, the Lebesgue measure, and multivariate polynomials, as well as a library for tensor analysis...