Suhui Liu | Searcharxiv

arXiv2021

$Γ-Σ-C^{0}-$determinacy of $Γ-Σ-C^{0}-$equivariant bifurcation problems with respect to $Γ-Σ-C^{0}-$BD and contact equivalence from the weighted point view

In this paper, $C^{0}$ finite determination of $Γ-$equivariant bifurcation problems in the relative case from the weighted point view is being discussed . Some criteria on the $C^{0}$ finite determination of $Γ-$equi-variant bifurcation problems in the relative case are then obtained in terms of an analytic-geometric non-degeneracy condition, which generalize the result on the $C^{0}$ finite determination of bifurcation problems given by P.B.Percell and P.N.Brown.

math.AG↗

arXiv2015

Projected Wirtinger Gradient Descent for Low-Rank Hankel Matrix Completion in Spectral Compressed Sensing

This paper considers reconstructing a spectrally sparse signal from a small number of randomly observed time-domain samples. The signal of interest is a linear combination of complex sinusoids at $R$ distinct frequencies. The frequencies can assume any continuous values in the normalized frequency domain $[0,1)$. After converting the spectrally sparse signal recovery into a low rank structured matrix completion problem, we propose an efficient feasible point approach, named projected Wirtinger gradient descent (PWGD) algorithm, to efficiently solve this structured matrix completion problem. We further accelerate our proposed algorithm by a scheme inspired by FISTA. We give the convergence analysis of our proposed algorithms. Extensive numerical experiments are provided to illustrate the efficiency of our proposed algorithm. Different from earlier approaches, our algorithm can solve problems of very large dimensions very efficiently.

cs.IT↗