20 citations · 22 across the 7 of their papers we have counts for
7 papers · 1 filter
Hermitian Quaternion Toeplitz Matrices by Quaternion-valued Generating Functions
Xue-lei Lin, Michael K. Ng, Junjun Pan
In this paper, we study Hermitian quaternion Toeplitz matrices generated by quaternion-valued functions. We show that such generating function must be the sum of a real-valued func…
A single-sided all-at-once preconditioning for linear system from a non-local evolutionary equation with weakly singular kernels
Xuelei Lin, Jiamei Dong, Sean Hon
{In [X. L. Lin, M. K. Ng, and Y. Zhi. {\it J. Comput. Phys.}, 434 (2021), pp. 110221] and [Y. L. Zhao, J. Wu, X. M. Gu, and H. Li. {\it Comput. Math. Appl.}, 148(2023), pp. 200--21…
A -preconditioner for space fractional diffusion equation with non-separable variable coefficients
Xue-Lei Lin, Michael K. Ng
In this paper, we study a -matrix approximation based preconditioner for the linear systems arising from discretization of unsteady state Riesz space fractional diffusion equati…
A parallel-in-time preconditioner for Crank-Nicolson discretization of a parabolic optimal control problem
Xue-Lei Lin, Shu-Lin Wu
In this paper, a fast solver is studied for saddle point system arising from a second-order Crank-Nicolson discretization of an initial-valued parabolic PDE constrained optimal con…
Spectral analysis for preconditioning of multi-dimensional Riesz fractional diffusion equations
Xin Huang, Xue-Lei Lin, Michael K. Ng +1
In this paper, we analyze the spectra of the preconditioned matrices arising from discretized multi-dimensional Riesz spatial fractional diffusion equations. The finite difference…
A parallel-in-time two-sided preconditioning for all-at-once system from a non-local evolutionary equation with weakly singular kernel
Xue-lei Lin, Michael K. Ng, Yajing Zhi
In this paper, we study a parallel-in-time (PinT) algorithm for all-at-once system from a non-local evolutionary equation with weakly singular kernel where the temporal term involv…
An efficient second-order convergent scheme for one-side space fractional diffusion equations with variable coefficients
Xue-lei Lin, Pin Lyu, Michael K. Ng +2
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing sch…