Calculating the singular values and pseudo-inverse of a matrix

By Gene H. Golub, W. Kahan. 2007

1,545 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Statistical and Nonlinear Physics

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Citations in the corpus

Variational Autoencoders Pursue PCA Directions (by Accident) (2018, neutral): “Theorem 1 (SVD rephrased, [13]) .”
Optimal combination forecasts for hierarchical time series (2011, methodology): “This method was primarily developed for solving a system of linear equations but was subsequently extended by Golub & Kahan (1965) to work with least squares problems with lower bidiagonalization of the coefficient matrix.”
Private traits and attributes are predictable from digital records of human behavior (2013, methodology): “Inbothcases,weapplied10-foldcross-validationandusedthe k = 100topSVDcomponents.”
TOPSIG: topology preserving document signatures (2011, methodology): “This is a signi.cant advantage over LSA whose time complexity is prohibitive in large collections.”
Singular value decomposition and least squares solutions (1970, background): “It was shown in [ 6 ] how to construct two finite sequences of Householder transformations”
Handbook of Big Data (2016, methodology): “The foundation is based on the commonly used Golub–Kahan–Lanczos bidiagonalization (GKLB) procedure [9], which is described in detail in Section 8.”
Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case (2010, background): “One of them in the Lanczos bidiagonalization, see [12] and Alg.”
MIMO Transceiver Design via Majorization Theory (2007, methodology): “For comparison, reduction of H to bidiagonal form by the Golub–Kahan bidiagonalization scheme [51] (also see [52, 56, 167]), often the first step in the computation of the SVD, requires O(mnK) flops.”
Structural damage detection by a new iterative regularization method and an improved sensitivity function (2017, methodology): “In a similar way, the RLSMR method utilizes the bidiagonalization algorithm proposed by Golub and Kahan [39].”
PCA: The Basic Building Block of Chemometrics (2012, methodology): “There are many variants of the SVD algorithm; the most well-known is probably the Golub-Reinsch algorithm [GR-SVD] [21, 22].”
Estimating Linear Models for Compositional Distributional Semantics (2010, methodology): “The algorithm for computing the singular value decomposition is iterative (Golub and Kahan, 1965).”
Sorting variables by using informative vectors as a strategy for feature selection in multivariate regression (2009, methodology): “Manne [24] has shown that PLS1 is equivalent to an algorithm developed by Golub and Kahan [25] for matrix bidiagonalization.”
The Optimal Hard Threshold for Singular Values is $4/\sqrt {3}$ (2014, background): “Date of publication June 30, 2014, date of current version July 10, 2014.”
A Krylov–Schur approach to the truncated SVD (2012, methodology): “Based on Stewart's technique we introduce a new factorization that will allow us to deflate certain singular values in the bidiagonalization process proposed by Golub and Kahan (cf. [9].”
Structured Lexical Similarity via Convolution Kernels on Dependency Trees (2011, methodology): “The original word-by-word context matrix M is decomposed through Singular Value Decomposition (SVD) (Golub and Kahan, 1965) into the product of three new matrices: U , S, and V so that S is diagonal and M = USV T .”