Matrix Computations, 3rd Edition

By Golub Gene H. Et.Al. 2007

1,024 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7c5526b67530484023f29fbfa6b39cb5d841b4df

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Citations in the corpus

The Relationships Among Various Nonnegative Matrix Factorization Methods for Clustering (2006, methodology): “SVD: The classic matrix factorization is Principal Component Analysis (PCA) which uses the singular value decomposition [?, 17], X ≈ UΣV T , where we allow U,V to have mixed-signs; the input data could have mixed-signs. absorbing Σ into U, we can write SVD: X ± ≈ U ± V ± 2.”
The subspace Gaussian mixture model - A structured model for speech recognition (2011, methodology): “Identifying null-spaces of matrices is hard in the presence of roundoff errors [15], so we use a method that does this in a soft manner without explicitly identifying the null-space (Appendix A).”
Population Structure and Eigenanalysis (2006, methodology): “Now we carry out a singular value decomposition on the matrix M. (A standard reference for the numerical methods is [ 19 ].”
Reduced-order optimal control of water flooding using proper orthogonal decomposition (2006, methodology): “We may, alternatively, compute the eigenvectors 8 8 with the aid of the singular value decomposition of the data matrix [ 4 ]:”
R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization (2006, background): “This is precisely the principal subspace of Cr. There exists a well-known subspace iteration algorithm in matrix theory ( Golub & Van Loan, 1996 ) that can e‐ciently compute the principal subspace.”
Diffusion Adaptation Strategies for Distributed Optimization and Learning Over Networks (2011, unknown): “Approximation (9) is reasonable since, in view of the Rayleigh-Ritz characterization of eigenvalues [47], we can always bound the weighted squared norm ‖w − wo‖2Γl by the unweighted squared norm as follows λmin(Γl) · ‖w−w‖(2) ≤ ‖w−wo‖2Γl ≤ λmax(Γl) · ‖w−w ‖(2) Thus, we replace (8) by J ′′ k (w) , J ”
A review of numerical methods for nonlinear partial differential equations (2012, unknown): “…variational formulation of the minimal surface equation, (2.3b), realized over a two-dimensional triangulation { T j } of a domain Ω, yields [115, 43] W Δ = arg min The minimizers sought above can be found by standard iterative algorithms, such as conjugate gradient and Krylov-based methods [92].”