• UTV

  • Referenced in 272 articles [sw05213]
  • interference-type problems with a rank-deficient covariance matrix, and we provide a robust ... dominant singular values of a sparse or structured matrix. These new algorithms have applications...
  • SDPT3

  • Referenced in 707 articles [sw04009]
  • case of determinant maximization problems with linear matrix inequalities. It employs an infeasible primal-dual ... block diagonal structure are exploited. We also exploit low-rank structures in the constraint matrices...
  • Manopt

  • Referenced in 124 articles [sw08493]
  • Such structured constraints appear pervasively in machine learning applications, including low-rank matrix completion, sensor...
  • SuiteSparseQR

  • Referenced in 45 articles [sw07348]
  • Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization. SuiteSparseQR is a sparse ... multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method ... eliminates singletons by permuting the input matrix A into the form ... matrix structures are found without requiring the formation of the pattern of ATA. Approximate rank...
  • Tensorlab

  • Referenced in 77 articles [sw14255]
  • define your own (coupled) matrix and tensor factorizations with structured factors and support for dense ... block term decompositions (BTD) and low multilinear rank approximation (LMLRA), complex optimization: quasi-Newton...
  • TensorToolbox

  • Referenced in 185 articles [sw04185]
  • array, and we consider how specially structured tensors allow for efficient storage and computation. First ... dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor ... expressed as the sum of rank-1 tensors. We are interested in the case where...
  • MSCRA_rankmin

  • Referenced in 3 articles [sw37064]
  • convex relaxation approach to noisy structured low-rank matrix recovery. This paper concerns with ... noisy structured low-rank matrix recovery problem which can be modeled as a structured rank ... experiments are conducted for some structured low-rank matrix recovery examples to confirm our theoretical...
  • LOBPCG

  • Referenced in 33 articles [sw09638]
  • Preconditioned low-rank methods for high-dimensional elliptic PDE eigenvalue problems. We consider elliptic ... that the resulting matrix eigenvalue problem Ax=λx exhibits Kronecker product structure. In particular ... where standard approaches to the solution of matrix eigenvalue problems fail due to the exponentially ... desired solution vector x in a low-rank tensor format. In this paper...
  • SDPNAL+

  • Referenced in 63 articles [sw13239]
  • partial or full nonnegative constraints on the matrix variable. SDPNAL+ is a much enhanced version ... decomposition method for solving two-easy-block structured semidefinite programs”, Math. Program. Comput ... rank-1 tensor approximation problems constructed by J. Nie and L. Wang [SIAM J. Matrix...
  • MDL4BMF

  • Referenced in 7 articles [sw28420]
  • Among other tasks, matrix factorizations are often used to separate global structure from noise. This ... proper rank of the factorization, that is, to answer where fine-grained structure stops ... where noise starts. Boolean Matrix Factorization (BMF)—where data, factors, and matrix product are Boolean...
  • NLEIGS

  • Referenced in 34 articles [sw22547]
  • generalized eigenvalue problem with special structure. This structure is particularly suited for the rational Krylov ... computation of rational divided differences using matrix functions is presented. It is shown that NLEIGS ... target set, and it also features low-rank approximation techniques for increased computational efficiency. Small...
  • drsolve

  • Referenced in 7 articles [sw38376]
  • structure. This package provides a set of Matlab functions to solve linear systems whose matrix ... size and r is the displacement rank of the matrix...
  • Colibri

  • Referenced in 9 articles [sw12043]
  • graphs. Low-rank approximations of the adjacency matrix of a graph are essential in finding ... desirable to track the low-rank structure as the graph evolves over time, efficiently ... columns and/or rows of the sparse matrix. However, these approaches will typically produce overcomplete bases...
  • na31

  • Referenced in 9 articles [sw11500]
  • linear systems with reconstructible Cauchy-like structure, which requires O(rn 2 ) floating point operations ... size of the matrix and r its displacement rank. The solver is based ... augmented matrix, under some assumptions on the knots of the Cauchy-like matrix. It includes ... Vandermonde-like linear systems, as these structures can be reduced to Cauchy-like by fast...
  • SBmethod

  • Referenced in 12 articles [sw07710]
  • minimizing the maximum eigenvalue of an affine matrix function (real and symmetric). The code ... exploit structural properties of the matrices such as sparsity and low rank structure. The code...
  • TKPSVD

  • Referenced in 12 articles [sw28028]
  • generalize the matrix Kronecker product to tensors such that each factor ... orthogonal rank-1 terms is computed. We prove that for many different structured tensors...
  • TuckerMPI

  • Referenced in 3 articles [sw27856]
  • goal is compression of massive-scale grid-structured data, such as the multi-terabyte output ... matrix. The result is a low-rank approximation of the original tensor-structured data. Compression...
  • RSVDPACK

  • Referenced in 6 articles [sw13832]
  • article ”Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions,” N. Halko ... codes implement a number of low rank SVD computing routines for three different sets...
  • Hm-toolbox

  • Referenced in 7 articles [sw32776]
  • matrices. Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile ... fact much wider and includes, for example, matrix functions and eigenvalue problems. In this work ... maintains the favorable complexity of hierarchical low-rank matrices and offers, at the same time...
  • DiSMEC

  • Referenced in 4 articles [sw30154]
  • correlation among labels by embedding the label matrix to a low-dimensional linear sub-space ... diverse label spaces, structural assumptions such as low rank can be easily violated. In this ... make any low rank assumptions on the label matrix. Using double layer of parallelization, DiSMEC...