47 citations · 103 across the 9 of their papers we have counts for
9 papers
Multivariate Feedback Particle Filter via F-divergence and the Well-posedness of its Admissible Control Input
Xue Luo
In this paper, we shall first derive the admissible control input of the multivariate feedback particle filter (FPF) by minimizing the f-divergence of the posterior conditional den…
Addendum: 2D homogeneous solutions to the Euler equation
Xue Luo, Roman Shvydkoy
In this addendum note we fill in the gap left in \cite{ls} in the description of 2D homogeneous solutions to the stationary Euler system with the help of the results of \cite{sd}.…
Time-dependent Hermite-Galerkin spectral method and its applications
Xue Luo, Shing-Tung Yau, Stephen S. -T. Yau
A time-dependent Hermite-Galerkin spectral method (THGSM) is investigated in this paper for the nonlinear convection-diffusion equations in the unbounded domains. The time-dependen…
2D homogeneous solutions to the Euler equation
Xue Luo, Roman Shvydkoy
In this paper we study classification of homogeneous solutions to the stationary Euler equation with locally finite energy. Written in the form , $Ψ(r,θ) = r^λ…
On the quenching behavior of the MEMS with fringing field
Xue Luo, Stephen S. -T. Yau
The singular parabolic problem on a bounded domain of with Dirichlet boundary condition, models the Microele…
On Classification of Toric Surface Codes of Low Dimension
Xue Luo, Stephen S. -T. Yau, Mingyi Zhang +1
This work is a natural continuation of our previous work \cite{yz}. In this paper, we give a complete classification of toric surface codes of dimension less than or equal to 6, ex…
Hermite spectral method with hyperbolic cross approximations to high-dimensional parabolic PDEs
Xue Luo, Stephen S. -T. Yau
It is well-known that sparse grid algorithm has been widely accepted as an efficient tool to overcome the "curse of dimensionality" in some degree. In this note, we first give the…
Hermite spectral method to 1D forward Kolmogorov equation and its application to nonlinear filtering problems
Xue Luo, Stephen S. -T. Yau
In this paper, we investigate the Hermite spectral method (HSM) to numerically solve the forward Kolmogorov equation (FKE). A useful guideline of choosing the scaling factor of the…
Complete Real Time Solution of the General Nonlinear Filtering Problem without Memory
Xue Luo, Stephen S. -T. Yau
It is well known that the nonlinear filtering problem has important applications in both military and civil industries. The central problem of nonlinear filtering is to solve the D…