The Schur complement and its applications

By Fuzhen Zhang. 2005

1,929 citations recorded by the source corpus.

Subfields: Ecology, Evolution, Behavior and Systematics, Optimization & Training

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Citations in the corpus

Negative Momentum for Improved Game Dynamics (2018, methodology): “See (Zhang, 2006, Section 0.3).”
Deep Learning without Poor Local Minima (2016, methodology): “Thus, by plugging in the formulas of Here, we can replace Accordingly, the ﬁrst term is reduced to zero as Zhang, 2006, p. 41).”
On Kernelized Multi-armed Bandits (2017, methodology): “Recursive Updates of Posterior Mean and Covariance We now describe a procedure to update the posterior mean and covariance function in a recursive fashion through the properties of Schur complement (Zhang (2006)) rather than evaluating Equation 2 and 3 at each round.”
Cramér-Rao Bound Optimization for Joint Radar-Communication Beamforming (2021, background): “By leveraging the following Schur complement condition [37] tr ˙A H ˙AR X − t − (cid:12)(cid:12)(cid:12) tr ˙A H AR X problem (54) can be rewritten as (29), which completes the proof.”
Extension of a result of Haynsworth and Hartfiel (2014, background): “We refer the readers to [14] for a survey of this important notion and its far reaching applications in various branches of mathematics.”
Spectra of the neighbourhood corona of two graphs (2012, neutral): “S = xIn1 −A(G1)− (1Tn2 ⊗A(G1)) ((xIn2 −A(G2))⊗ In1) −1 (1n2 ⊗A(G1)) is the Schur complement [18] of (xIn2 −A(G2))⊗ In1 .”
Spectra of subdivision-vertex and subdivision-edge neighbourhood coronae (2012, background): “where M1−M2M 4 M3 and M4−M3M −1 1 M2 are called the Schur complements [18] of M4 and M1, respectively.”
Kronecker-factored Curvature Approximations for Recurrent Neural Networks (2018, background): “Note that the Schur complement is PSD because the original block matrix itself is (e.g. Zhang, 2006).”
Models, feedback control, and open problems of 3D bipedal robotic walking (2014, methodology): “Block matrix inversion can be performed using the Schur complement (see [227]) to obtain a direct expression for post-impact velocity, namely”
On the phases of a complex matrix (2019, background): “If C11 is nonsingular, then the Schur complement [17] of C11 in C, denoted by C/11, exists and is given by C/11 = C22 − C21C 11 C12.”