Computational Methods for Linear Matrix Equations

By Valeria Simoncini. SIAM Review, 2016

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The general $\phi$-Hermitian solution to mixed pairs of quaternion matrix Sylvester equations (2017, unknown): “[2]–[11], [18]–[20], [22], [28]–[30], [39]–[43], [48]).”
Optimizing Neural Networks with Kronecker-factored Approximate Curvature (2015, methodology): “As our baseline we used the version of SGD with momentum based on Nesterov’s Accelerated Gradient (Nesterov, 1983) described in Sutskever et al. (2013), which was calibrated to work well on these particular deep autoencoder problems. For each problem we followed the prescription given by Sutskever e”
A Two-pronged Progress in Structured Dense Matrix Vector Multiplication (2018, background): “Such equations are very difficult to analyze in full generality [50], and our notions represent one line of attack for efficient solutions to these problems.”
Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations (2014, background): “It can be shown that when the rank of the right-hand sideR of these equations is much lower than the dimension of the equations, i.e.,rankR ≪ min(n, r), the solution often exhibits a low numerical rank [1, 19, 28, 29, 34].”
On critical points of quadratic low-rank matrix optimization problems (2020, methodology): “To obtain such approximations, there exists a few methods that are built from classical solvers in numerical linear algebra, like the ADI and Krylov methods; see [28] for a recent overview.”