Jianwei Zhou

Enze Yuan, Huantian Xie, Ziwu Jiang et al.

A novel collocation scheme is presented for elliptic-type differential equations with degenerate coefficients and homogeneous Dirichlet boundary conditions. The use of weighted orthogonal Chebyshev polynomials for the basis functions leads to stiffness matrices with sparse structure, enabling efficient direct calculations. By an orthogonal projection, rigorous analyses are devoted to deriving a-priori error estimates of spectral accuracy in two norms. Furthermore, ample numerical experiments are conducted and compared with error data, convergence rates, condition numbers and $N$-$\log$ curves to confirm the theoretical analyses results. Our proposed method achieves spectral accuracy and handles boundary singularities efficiently, as demonstrated by theoretical analyses and numerical experiments.

Mengxue Gao, Bing Su, Jianwei Zhou

A novel mixed spectral-Galerkin method based on generalized ball polynomials is proposed for solving the biharmonic equation on a unit ball. By introducing an auxiliary variable to decouple the biharmonic equation into a system of second-order equations, the corresponding discrete scheme yields a strictly diagonal stiffness matrix, which significantly enhances the computational efficiency. Rigorous a-priori error estimates are established to demonstrate the exponential convergence rates in both the $L^2$- and $H^1$-norms. Extensive numerical experiments are conducted to verify the theoretical analysis and confirm the high efficiency and accuracy of the proposed scheme.

Jianwei Zhou, Zhaolin Jiang

In this paper we investigate the spectral norm for circulant matrices, whose entries are modified Fibonacci numbers and Lucas numbers. We obtain the identity estimations for the spectral norms. Some numerical test results are listed to verify the results using those approaches.

Yan Yin, Ramon Prieto, Bin Wang et al.

Recent research has shown that attention-based sequence-to-sequence models such as Listen, Attend, and Spell (LAS) yield comparable results to state-of-the-art ASR systems on various tasks. In this paper, we describe the development of such a system and demonstrate its performance on two tasks: first we achieve a new state-of-the-art word error rate of 3.43% on the test clean subset of LibriSpeech English data; second on non-native English speech, including both read speech and spontaneous speech, we obtain very competitive results compared to a conventional system built with the most updated Kaldi recipe.