Zobrazeno 1 - 10
of 73
pro vyhledávání: '"Hon, Sean"'
In this work, we propose a novel diagonalization-based preconditioner for the all-at-once linear system arising from the optimal control problem of parabolic equations. The proposed preconditioner is constructed based on an $\epsilon$-circulant modif
Externí odkaz:
http://arxiv.org/abs/2410.22686
In recent years, there has been a renewed interest in preconditioning for multilevel Toeplitz systems, a research field that has been extensively explored over the past several decades. This work introduces novel preconditioning strategies using mult
Externí odkaz:
http://arxiv.org/abs/2409.20363
Preconditioning for multilevel Toeplitz systems has long been a focal point of research in numerical linear algebra. In this work, we develop a novel preconditioning method for a class of nonsymmetric multilevel Toeplitz systems, which includes the a
Externí odkaz:
http://arxiv.org/abs/2409.15770
In this study, the $\theta$-method is used for discretizing a class of evolutionary partial differential equations. Then, we transform the resultant all-at-once linear system and introduce a novel one-sided preconditioner, which can be fast implement
Externí odkaz:
http://arxiv.org/abs/2408.03535
The complex-shifted Laplacian systems arising in a wide range of applications. In this work, we propose an absolute-value based preconditioner for solving the complex-shifted Laplacian system. In our approach, the complex-shifted Laplacian system is
Externí odkaz:
http://arxiv.org/abs/2408.00488
Autor:
Li, Congcong, Hon, Sean
In this work, we develop a novel multilevel Tau matrix-based preconditioned method for a class of non-symmetric multilevel Toeplitz systems. This method not only accounts for but also improves upon an ideal preconditioner pioneered by [J. Pestana. Pr
Externí odkaz:
http://arxiv.org/abs/2407.19386
Autor:
Fung, Po Yin, Hon, Sean
In this work, we propose a class of novel preconditioned Krylov subspace methods for solving an optimal control problem of parabolic equations. Namely, we develop a family of block $\omega$-circulant based preconditioners for the all-at-once linear s
Externí odkaz:
http://arxiv.org/abs/2406.00952
A novel fourth-order finite difference formula coupling the Crank-Nicolson explicit linearized method is proposed to solve Riesz space fractional nonlinear reaction-diffusion equations in two dimensions. Theoretically, under the Lipschitz assumption
Externí odkaz:
http://arxiv.org/abs/2405.03143
{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--210]}, two-sided preconditioning techniques are proposed for non-local e
Externí odkaz:
http://arxiv.org/abs/2404.13974
In this work, we propose a novel preconditioned Krylov subspace method for solving an optimal control problem of wave equations, after explicitly identifying the asymptotic spectral distribution of the involved sequence of linear coefficient matrices
Externí odkaz:
http://arxiv.org/abs/2307.12850