Numerical Methods for Simultaneous Diagonalization

By A. Bunse-Gerstner, Ralph Byers, Volker Mehrmann. 1993

Subfields: Numerical Methods & Scientific Computing

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Citations in the corpus

Beyond CCA: Moment Matching for Multi-View Models (2016, neutral): “Therefore, the workhorses of the method of moments in similar context — orthogonal diagonalization algorithms, such as the tensor power method (Anandkumar et al., 2014), and orthogonal joint diagonalization (Bunse-Gerstner et al., 1993; Cardoso & Souloumiac, 1996) — are not applicable.”
Rethinking LDA: Moment Matching for Discrete ICA (2015, neutral): “Importantly, a fast implementation [23] of the orthogonal joint diagonalization algorithm from [24] was proposed, which is based on closed-form iterative Jacobi updates (see, e.”
Tensor decompositions for learning latent variable models (2012, methodology): “Related simultaneous diagonalization approaches have also been used for blind source separation and ICA (as discussed above), and a number of efficient algorithms have been developed for this problem (Bunse-Gerstner et al., 1993; Cardoso and Souloumiac, 1993; Cardoso, 1994; Cardoso and Comon, 1996; ”
A Spectral Algorithm for Latent Dirichlet Allocation (2012, methodology): “It should be noted that there are other methods in the literature for obta ining these decompositions, for instance, methods based on simultaneous diagonalizations of matrice s [36] as well as direct tensor decomposition methods [37]; and that these methods can be signific a tly more stable than Alg”
Monarch: Expressive Structured Matrices for Efficient and Accurate Training (2022, methodology): “see (Conrad; Bunse-Gerstner et al., 1993)): first, set i = 1 and diagonalize the first matrix Gi = G1 (i.”
Learning mixtures of spherical gaussians: moment methods and spectral decompositions (2012, methodology): “It is also possible to use, for instance, simultaneous diagonalization techniques [7] or orthogonal tensor decompositions [2] to extract the parameters from (estimates of) M2 and M3; these alternative methods are more robust to sampling error, and are therefore recommended for practical implementati”
Multimodal Manifold Analysis by Simultaneous Diagonalization of Laplacians (2015, unknown): “Such methods have received limited attention in the numerical mathematics community [19] and in blind source separation applications [20], [21], [22], [23].”
Simultaneous Diagonalization With Similarity Transformation for Non-Defective Matrices (2006, unknown): “1 of [10], by the observation that (19) is π/2 periodic in θ, we can constrain θ ∈ [−π/4, π/4).”
Adaptive blind signal and image processing (2002, methodology): “The objective of this procedure is to find the orthogonal matrix U which diagonalizes a set of matrices [120, 870, 1389]: Mi = UDiU + εi, (i = 1, 2, .”
Tensor Factorization via Matrix Factorization (2015, unknown): “Empirically though, these algorithms have been found in the literature to converge reliably to global minima [27, 25, 30] and to corroborate this claim, we conducted a series of experiments [16].”