3 citations · 6 across the 9 of their papers we have counts for
9 papers
Global monotone convergence of Newton-like iteration for a nonlinear eigen-problem
Peichang Guo
The nonlinear eigen-problem is studied where is an irreducible Stieltjes matrix. Under certain conditions, this problem has a unique positive solution…
Regularization for convolutional kernel tensors to avoid unstable gradient problem in convolutional neural networks
Pei-Chang Guo
Convolutional neural networks are very popular nowadays. Training neural networks is not an easy task. Each convolution corresponds to a structured transformation matrix. In order…
A Frobenius norm regularization method for convolutional kernels to avoid unstable gradient problem
Pei-Chang Guo
Convolutional neural network is a very important model of deep learning. It can help avoid the exploding/vanishing gradient problem and improve the generalizability of a neural net…
On regularization for a convolutional kernel in neural networks
Peichang Guo, Qiang Ye
Convolutional neural network is an important model in deep learning. To avoid exploding/vanishing gradient problems and to improve the generalizability of a neural network, it is d…
A modified Newton method for multilinear PageRank
Pei-Chang Guo
When studying the multilinear PageRank problem, a system of polynomial equations needs to be solved. In this paper, we develop convergence theory for a modified Newton method in a…
A fast Newton-Shamanskii iteration for M/G/1-type and GI/M/1-type Markov chains
Pei-Chang Guo
For the nonlinear matrix equations arising in the analysis of M/G/1-type and GI/M/1-type Markov chains, the minimal nonnegative solution or can be found by Newton-like meth…
A modified large-scale structure-preserving doubling algorithm for a large-scale Riccati equation from transport theory
Peichang Guo
We consider the large scale nonsymmetric algebraic Riccati equation arising in transport theory, where the coefficient matrices are symmetric and low-ranked and…
Perturbation analysis of the extinction probability of a Markovian binary tree
Peichang Guo
The extinction probability of the Markovian Binary Tree (MBT) is the minimal nonnegative solution of a Quadratic Vector Equation (QVE). In this paper, we present a perturbation ana…
The Newton-Shamanskii method for solving a quadratic matrix equation arising in quasi-birth-death problems
Peichang Guo
In order to determine the stationary distribution for discrete time quasi-birth-death Markov chains, it is necessary to find the minimal nonnegative solution of a quadratic matrix…