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- Sheng-Long Hu, Zheng-Hai Huang, Qiong Zhang
- J. Computational Applied Mathematics
- 2009

A direct generalized Newton method is proposed for solving the NP-hard absolute value equation (AVE) Ax−|x| = b when the singular values of A exceed 1. A simple MATLAB implementation of the method solved 100 randomly generated 1000-dimensional AVEs to an accuracy of 10 −6 in less than 10 seconds each. Similarly, AVEs corresponding to 100 randomly generated… (More)

- Sheng-Long Hu, Zheng-Hai Huang
- Optimization Letters
- 2010

- Sheng-Long Hu, Liqun Qi
- J. Comb. Optim.
- 2012

- Sheng-Long Hu, Liqun Qi
- J. Comb. Optim.
- 2015

In this paper, we investigate the Laplacian, i.e., the normalized Laplacian tensor of a k-uniform hypergraph. We show that the real parts of all the eigenvalues of the Laplacian are in the interval [0, 2], and the real part is zero (respectively two) if and only if the eigenvalue is zero (respectively two). All the H +-eigenvalues of the Laplacian and all… (More)

- Sheng-Long Hu, Guoyin Li, Liqun Qi, Yisheng Song
- J. Optimization Theory and Applications
- 2013

Finding the maximum eigenvalue of a tensor is an important topic in tensor computation and multilinear algebra. Recently, for a tensor with nonnegative entries (which we refer it as a nonnegative tensor), efficient numerical schemes have been proposed to calculate its maximum eigenvalue based on a Perron–Frobenius-type theorem. In this paper, we consider a… (More)

- Sheng-Long Hu, Liqun Qi
- Discrete Applied Mathematics
- 2014

In this paper, we show that the eigenvectors associated with the zero eigenval-ues of the Laplacian and signless Lapacian tensors of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector associated with the zero eigenvalue of the Laplacian or signless Lapacian tensor have… (More)

- Sheng-Long Hu, Zheng-Hai Huang, Nan Lu
- J. Sci. Comput.
- 2010

The monotone line search schemes have been extensively used in the iterative methods for solving various optimization problems. It is well known that the non-monotone line search technique can improve the likelihood of finding a global optimal solution and the numerical performance of the methods, especially for some difficult nonlinear problems. The… (More)

- Sheng-Long Hu, Zheng-Hai Huang, Chen Ling, Liqun Qi
- J. Symb. Comput.
- 2013

- Sheng-Long Hu, Zheng-Hai Huang, Liqun Qi
- Numerical Lin. Alg. with Applic.
- 2013

- Sheng-Long Hu, Liqun Qi
- Applied Mathematics and Computation
- 2014