Matrices: Theory and Applications

By Denis Serre. 2002

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Citations in the corpus

Telling cause from effect in deterministic linear dynamical systems (2015, background): “[22] For a given Hermitian matrix H and any principal submatrix of H , H ′ , their spectral radius ρ s satisﬁes ) → R f ∈ L 1 be a bounded function and suppose t k is its Fourier series coeﬃcients, i.e.”
Weighted extreme learning machine for imbalance learning (2013, unknown): “The least square solution with minimal norm is analytically determined using Moore–Penrose ‘‘generalized’’ inverse Ĥ [12,13]:”
Extreme learning machine: RBF network case (2004, methodology): “…than the number of distinct training samples, ˜ N N , H is a nonsquare matrix and there may not exist w i , b i , which is equivalent to minimizing the cost function ⎝ ⎠ When H is unknown gradient-based learning algorithms are generally used to search the minimum of H β − T . gradient-based In the…”
Extreme Learning Machine for Regression and Multiclass Classification (2012, methodology): “The minimal norm least square method instead of the standard optimization method was used in the original implementation of ELM [12], [13] where H † is the Moore–Penrose generalized inverse of matrix H [35], [36].”
Voting based extreme learning machine (2012, background): “where H is the Moore–Penrose generalized inverse [30] of the hidden layer output matrix H.”
Extreme learning machines: a survey (2011, unknown): “b̂ 1⁄4 HyT ð16Þ where Hy is the Moore–Penrose generalized inverse of matrix H [37, 38].”
Nil-clean matrix rings (2013, background): “For a background material concerning matrix theory that will be used in the sequel without a concrete citation, we refer to [6].”
Bayesian density regression (2007, background): “Proof of lemma 3: B D ( D 1( In C)) 1 has non-negative entries Our main argument for the proof of lemma 3 is the following lemma from Serre (2002), page 80.”
Extreme learning machine: a new learning scheme of feedforward neural networks (2004, methodology): “The resolution of a general linear systemAx = y, where A may be singular and may even not be square, can be made very simple by the use of the Moore-Penrose generalized inverse[10].”
Extreme learning machine: Theory and applications (2006, methodology): “where Hy is the Moore–Penrose generalized inverse of matrix H [22,19].”