Matrix computations

By Gene H. Golub. 1983

Subfields: Numerical Methods & Scientific Computing

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “For d = 2 all these schemes boil down to the well known reduced singular value decomposition (SVD) of matrices [98]; however, they differ significantly for tensors of order d ≥ 3.”
Optimization Methods for Large-Scale Machine Learning (2016, methodology): “r than solve the Newton system (6.4b) exactly through matrix factorization techniques, one can instead only solve it inexactly through an iterative approach such as the conjugate gradient (CG) method [69]. By ensuring that the linear solves are accurate enough, such an inexact Newton-CG method can e”
Don’t count, predict! A systematic comparison of context-counting vs. context-predicting semantic vectors (2014, methodology): “The latter were obtained by applying the Singular Value Decomposition (Golub and Van Loan, 1996) or Non-negative Matrix Factorization (Lee and Seung, 2000), Lin (2007) algorithm, with reduced sizes ranging from 200 to 500 in steps of 100.”
Making AI Forget You: Data Deletion in Machine Learning (2019, methodology): “[83] C.”
Benign overfitting in linear regression (2019, neutral): “[23] Gene H.”
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions (2009, methodology): “algorithm may depend on all these factors [13, 61, 133].”
Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation (2004, unknown): “Singular value decomposition (SVD) In this section, we give a brief description of the SVD and for further details see References [16, 17].”
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images (2009, methodology): “For this sub-matrix a rank-1 approximation via SVD [82] can be applied, updating both the atom aj0 and the coefficients that deploy it to the sparse representations.”
Fast Random Walk Graph Kernel (2012, methodology): “For static graphs, the most popular choices include SVD/PCA [12, 19] and random projection [17].”
Kernel independent component analysis (2003, background): “Symmetric permutations of rows and columns are necessary during the factorization if we require the rank to be as small as possible (Golub and Loan, 1983).”
Information Bottleneck for Gaussian Variables (2003, methodology): “It thus has similar form to the power method for calculating the dominant eigenvectors of the matrix Σy|xΣ x (Demmel, 1997; Golub and Loan, 1989).”