209 citations · 1.4k across the 114 of their papers we have counts for
5 papers · 1 filter
Convergence of Oja's online principal component flow
Jian-Guo Liu, Zibu Liu
Online principal component analysis (PCA) has been an efficient tool in practice to reduce dimension. However, convergence properties of the corresponding ODE are still unknown, in…
A note on one-dimensional time fractional ODEs
Yuanyuan Feng, Lei Li, Jian-Guo Liu +1
In this note, we prove or re-prove several important results regarding one dimensional time fractional ODEs following our previous work \cite{fllx17}. Here we use the definition of…
Continuous and discrete one dimensional autonomous fractional ODEs
Yuanyuan Feng, Lei Li, Jian-Guo Liu +1
In this paper, we study 1D autonomous fractional ODEs , where is the unknown function and is the generalized Caputo de…
A generalized definition of Caputo derivatives and its application to fractional ODEs
Lei Li, Jian-Guo Liu
We extend in this paper the definition of Caputo derivatives of order in to a certain class of locally integrable functions using a convolution group. Our strategy is to de…
On generating functions of Hausdorff moment sequences
Jian-Guo Liu, Robert L. Pego
The class of generating functions for completely monotone sequences (moments of finite positive measures on ) has an elegant characterization as the class of Pick functions…