48 citations · 95 across the 15 of their papers we have counts for
15 papers
Exact self-similar finite-time blowup of the Hou-Luo model with smooth profiles
De Huang, Xiang Qin, Xiuyuan Wang +1
We show that the 1D Hou-Luo model on the real line admits exact self-similar finite-time blowup solutions with smooth self-similar profiles. The existence of these profiles is esta…
Self-similar finite-time blowups with smooth profiles of the generalized Constantin-Lax-Majda model
De Huang, Xiang Qin, Xiuyuan Wang +1
We show that the -parameterized family of the generalized Constantin-Lax-Majda model, also known as the Okamoto-Sakajo-Wunsch model, admits exact self-similar finite-time blowup…
On self-similar finite-time blowups of the De Gregorio model on the real line
De Huang, Jiajun Tong, Dongyi Wei
We show that the De Gregorio model on the real line admits infinitely many compactly supported, self-similar solutions that are distinct under rescaling and will blow up in finite…
Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations
Jiajie Chen, Thomas Y. Hou, De Huang
Inspired by the numerical evidence of a potential 3D Euler singularity \cite{luo2014potentially,luo2013potentially-2}, we prove finite time singularity from smooth initial data for…
Streaming k-PCA: Efficient guarantees for Oja's algorithm, beyond rank-one updates
De Huang, Jonathan Niles-Weed, Rachel Ward
We analyze Oja's algorithm for streaming -PCA and prove that it achieves performance nearly matching that of an optimal offline algorithm. Given access to a sequence of i.i.d. $…
Nonlinear Matrix Concentration via Semigroup Methods
De Huang, Joel A. Tropp
Matrix concentration inequalities provide information about the probability that a random matrix is close to its expectation with respect to the operator norm. This paper use…
From Poincaré Inequalities to Nonlinear Matrix Concentration
De Huang, Joel A. Tropp
This paper deduces exponential matrix concentration from a Poincaré inequality via a short, conceptual argument. Among other examples, this theory applies to matrix-valued function…
Matrix Concentration for Products
De Huang, Jonathan Niles-Weed, Joel A. Tropp +1
This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize recent work of Henriksen-Ward,…
Generality of Lieb's Concavity Theorem
De Huang
We show that Lieb's concavity theorem holds more generally for any unitarily invariant matrix function that is monotone and concave. Concre…
Improvement on a Generalized Lieb's Concavity Theorem
De Huang
We show that Lieb's concavity theorem holds more generally for any unitary invariant matrix function that is concave and satisfies Höld…
On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equation
Jiajie Chen, Thomas Y. Hou, De Huang
We present a novel method of analysis and prove finite time asymptotically self-similar blowup of the De Gregorio model \cite{DG90,DG96} for some smooth initial data on the real li…
Generalizing Lieb's Concavity Theorem via Operator Interpolation
De Huang
We introduce the notion of -trace and use interpolation of operators to prove the joint concavity of the function $(A,B)\mapsto\text{Tr}_k\big[(B^\frac{qs}{2}K^*A^{ps}KB^\frac{q…
A generalized Lieb's theorem and its applications to spectrum estimates for a sum of random matrices
De Huang
In this paper we prove the concavity of the -trace functions, , on the convex cone of all positive definite matrices. $\text{Tr}_k[A…
A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition
Thomas Y. Hou, De Huang, Ka Chun Lam +1
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 multireso…
An adaptive fast solver for a general class of positive definite matrices via energy decomposition
Thomas Y. Hou, D. Huang, K. C. Lam +1
In this paper, we propose an adaptive fast solver for a general class of symmetric positive definite (SPD) matrices which include the well-known graph Laplacian. We achieve this by…