Potential singularity formation of incompressible axisymmetric Euler equations with degenerate viscosity coefficients

no code implementations • 12 Feb 2021 • Thomas Y. Hou, De Huang

In this paper, we present strong numerical evidences that the incompressible axisymmetric Euler equations with degenerate viscosity coefficients and smooth initial data of finite energy develop a potential finite-time locally self-similar singularity at the origin.

Analysis of PDEs Numerical Analysis Numerical Analysis Fluid Dynamics 35Q30, 35Q31, 35A21

Streaming k-PCA: Efficient guarantees for Oja's algorithm, beyond rank-one updates

no code implementations • 6 Feb 2021 • De Huang, Jonathan Niles-Weed, Rachel Ward

We analyze Oja's algorithm for streaming $k$-PCA and prove that it achieves performance nearly matching that of an optimal offline algorithm.

A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition

no code implementations • 10 Apr 2018 • Thomas Y. Hou, De Huang, Ka Chun Lam, Ziyun Zhang

In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework.