Linear Algebra and its Applications

By Yunhui He, Jun Liu, Xiang Wang. 2010

provedthatamongalltreesoforder

Subfields: Numerical Methods & Scientific Computing

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Citations in the corpus

A Tight and Unified Analysis of Extragradient for a Whole Spectrum of Differentiable Games (2019, background): “See Lax (2007, p. 74) for instance.”
The uses of homogeneous barycentric coordinates in plane Euclidean geometry (2000, methodology): “The uses of homogeneous barycentric coordinates in plane Euclidean geometry PAUL YIU Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA; e-mail: yiu@ fau.edu (Received 25 Jaunary 1999 ) The notion of homogeneous barycentric coordinates provides a powerful…”
ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEs (2019, methodology): “As shown in [Shen, 2001], ‖W‖2 grows as √ n and numerically reversing this ODE is nearly impossible for n as small as 100 (it requires 10,000 time steps to get single precision accuracy in error defined by equation 6).”
Wiley‐Interscience Series in Discrete Mathematics and Optimization (2011, unknown): “For a more complete but still basic treatment of topics in linear algebra as discussed in this and the previous chapter, see [33], [47], [69], [91].”
Last Iterate is Slower than Averaged Iterate in Smooth Convex-Concave Saddle Point Problems (2020, unknown): “Therefore, by the spectral mapping theorem (see, e.g., (Lax, 2007, Theorem 4)), C 0 ( A ) has n/ 2 eigenvalues equal to each of q 0 ( νi ) and q 0 ( νi ) = q 0 ( νi ) .”
The Design of Approximation Algorithms (2011, unknown): “Strang [273, 274] provides introductions to linear algebra that are useful in the context of our discussion of semidefinite programming and various operations on vectors and matrices.”
Measures and applications of quantum correlations (2016, unknown): “Indeed, both are examples of geodesic distances belonging to a family of monotone and Riemannian metrics defined on the set of quantum states, characterised by the Morozova-Čentsov-Petz theorem [134, 135, 77].”
A Tight and Unified Analysis of Gradient-Based Methods for a Whole Spectrum of Differentiable Games (2020, background): “Then, See for instance Lax (2007, Theorem 4, p. 66 ) for a proof.”
Exact controllability of complex networks (2013, unknown): “Thus, it is reasonable to assume random-weight distributions rather denotes the minimum number of drivers calculated from the maximum algebraic multiplicity. q = 1 , 2 , · · · , N and the algebraic multiplicity of eigenvalues is indicated in “()” for star and fully connected networks.”
Bayesian reasoning and machine learning (2012, unknown): “This can be obtained more rapidly and with greater numerical precision using Gaussian elimination[274, 124].”
Handbook of Cluster Analysis (2015, unknown): “Recall a classic Rayleigh-Ritz theorem in linear algebra [43], stating that the sum of K Rayleigh quotients depending on orthogonal vectors y(1) .”
Functional, but Not Anatomical, Separation of "what" and "when" in Prefrontal Cortex Gaussian-process Factor Analysis for Low-dimensional Single-trial Analysis of Neural Population Activity (unknown): “The orthonormalization procedure involves applying the singular value decomposition (Strang 1988) to the learned C.”