Matrix analysis - for scientists and engineers

By A. Laub. 2004

906 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9f386c76f9c01e5f6d482a849bb554539f627750

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In Computational Theory and Mathematics

Citations in the corpus

KiPar, a tool for systematic information retrieval regarding parameters for kinetic modelling of yeast metabolic pathways (2009, neutral): “In addition, Humphreys concentration) related to the participants of metabolic reactions.”
Fast Random Walk Graph Kernel (2012, background): “where W is also symmetric by the nature of Kronecker products [23].”
Compressing RNNs for IoT devices by 15-38x using Kronecker Products (2019, background): “This is because of the following relationship (Laub, 2005) -”
Channel Estimation and Hybrid Precoding for Millimeter Wave Cellular Systems (2014, methodology): “…transmitted symbols are equal, namely, S = √ P I M BS and therefore To exploit the sparse nature of the channel, we ﬁrst vectorize the resultant matrix Y where ( a ) follows from [25, Theorem 13.26], ( b ) follows from the channel model in (6), and the properties of the Khatri-Rao product, [21].”
Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation (2014, background): “11), the symbol ⊗ is the Kronecker tensor product [59,60], also the coefficient matrix Ä is given in a block form as follows”
Non-linear Causal Inference using Gaussianity Measures (2014, methodology): “, d}n, |·| denotes absolute value, and we have employed standard properties of the Kronecker product about eigenvalues and eigenvectors (Laub, 2004).”
Linear convergence of primal-dual gradient methods and their performance in distributed optimization (2019, background): “Proof: Introduce the truncated singular value decomposition [30] of the positive semi-definite matrix BB = UrΣrU T r , where Ur ∈ RM×r (r denotes the rank of BB) with U r Ur = Ir and Σr > 0 is a diagonal matrix with entries equal to the non-zero eigenvalues of BB ( i.”
A new approach to cross-modal multimedia retrieval (2010, background): “GEVs can be solved as efficiently as regular eigenvalue problems [15].”
Novel Multidimensional Models of Opinion Dynamics in Social Networks (2015, methodology): “Lemma 1: [38] For any three matrices A , B , C such that the product ABC is deﬁned, one has In particular, for A ∈ R m × l and B ∈ R l × n one obtains The constraints in (30), (34) can be simpliﬁed.”
Diffusion Strategies Outperform Consensus Strategies for Distributed Estimation Over Adaptive Networks (2012, neutral): “1s T 1 Σvs1r T 1 ≥ 0 (184) Using (143), we conclude that det(Σv −r 1s T 1 Σvs1r T) = det(Σv) ·det IN −Σ−1 v 1· sT 1 Σvs1 N 1T ≥ 0 (185) Since for any column vectors {x,y} of size N, it holds that [40]: det(IN −x·yT) = 1−yT · x (186) relation (185) implies that the following must hold: 1− sT 1 Σvs”