On the Compression of Low Rank Matrices

By Hongwei Cheng, Zydrunas Gimbutas, Per-Gunnar Martinsson, Vladimir Rokhlin. SIAM Journal on Scientific Computing, 2005

370 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/12abcb004981dd44b839cfefb6e22147fa681356

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In Atomic and Molecular Physics, and Optics

In Computational Mechanics

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Citations in the corpus

Numerical construction of Green's functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations (2012, methodology): “The analytical framework from our approach comes from [37, 148, 100], in which the authors describe an algorithm for the interpolative decomposition (ID) of low rank matrices.”
Randomized numerical linear algebra: Foundations and algorithms (2020, background): “Moreover, it gives well-conditioned factorizations as long as orthonormality of the basis is scrupulously maintained (Martinsson et al. 2006b, Cheng et al. 2005).”
SketchOGD: Memory-Efficient Continual Learning (2023, neutral): “…setting of one-pass learning. b) Matrix approximation: Many approaches have been proposed for approximating or compressing a matrix, including techniques based on sparsification and quantization [26], column selection [27], dimensionality reduction [28] and approximation by submatrices [29].”
An algorithm for the rapid evaluation of special function transforms (2010, methodology): “2 In this paper, we use the numerical scheme for the computation of the matrix P described in [2].”
A fast algorithm for the inversion of general Toeplitz matrices (2004, methodology): “The statement of Observation 1 relies on the fact that has been precomputed for a given N and for a given hierarchical partitioning of the index set {1,..., N}. This can be accomplished in O(N21og 2 N) arithmetic operations using a standard rank-revealing QR-faetorization as described in [14, 15 ].”
The black-box fast multipole method (2009, methodology): “These techniques are often based on wavelet decompositions [4,5], singular value decompositions [6,7], or other schemes [2,8].”
Diffusion Wavelets (2004, methodology): “In [42,43] techniques for compressing low-rank matrices (see also [63]) are applied to the problem of obtaining an explicit sparse inverse, in particular for the solution of integral equations arising from boundary value problems of elliptic PDEs.”
A randomized algorithm for the decomposition of matrices (2011, neutral): “See, for example, [5] [8] [12] [18], or Sections 4 and 5 of [3] for a discussion of interpolative decompositions.”
A fast direct solver for boundary integral equations in two dimensions (2003, methodology): “The factorization technique described in this paper is a multilevel extension of the compression technique described in [10].”