Zobrazeno 1 - 10
of 75
pro vyhledávání: '"Kemmochi, Tomoya"'
This note considers the computation of the logarithm of symmetric positive definite matrices using the Gauss--Legendre (GL) quadrature. The GL quadrature becomes slow when the condition number of the given matrix is large. In this note, we propose a
Externí odkaz:
http://arxiv.org/abs/2410.22014
Publikováno v:
Special Matrices, Vol 12, Iss 1, Pp 970-989 (2024)
This article considers the computation of the matrix exponential eA{{\rm{e}}}^{A} with numerical quadrature. Although several quadrature-based algorithms have been proposed, they focus on (near) Hermitian matrices. In order to deal with non-Hermitian
Externí odkaz:
https://doaj.org/article/7c76cdb981cc4f7fa61c7c9f9fead7b9
Autor:
Kemmochi, Tomoya
Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For numerical com
Externí odkaz:
http://arxiv.org/abs/2308.02334
We consider the convolution equation $F*X=B$, where $F\in\mathbb{R}^{3\times 3}$ and $B\in\mathbb{R}^{m\times n}$ are given, and $X\in\mathbb{R}^{m\times n}$ is to be determined. The convolution equation can be regarded as a linear system with a coef
Externí odkaz:
http://arxiv.org/abs/2306.15359
Publikováno v:
Spec. Matrices, 12 (2024) 20240013
This paper considers the computation of the matrix exponential $\mathrm{e}^A$ with numerical quadrature. Although several quadrature-based algorithms have been proposed, they focus on (near) Hermitian matrices. In order to deal with non-Hermitian mat
Externí odkaz:
http://arxiv.org/abs/2306.14197
Maximal regularity is a kind of a priori estimates for parabolic-type equations and it plays an important role in the theory of nonlinear differential equations. The aim of this paper is to investigate the temporally discrete counterpart of maximal r
Externí odkaz:
http://arxiv.org/abs/2306.11365
Autor:
Kemmochi, Tomoya
Maximal regularity for the Stokes operator plays a crucial role in the theory of the non-stationary Navier--Stokes equations. In this paper, we consider the finite element semi-discretization of the non-stationary Stokes problem and establish the dis
Externí odkaz:
http://arxiv.org/abs/2303.16236
Autor:
Kemmochi, Tomoya, Miura, Tatsuya
Publikováno v:
J. Math. Pures Appl. 185 (2024), 47--62
Huisken's problem asks whether there is an elastic flow of closed planar curves that is initially contained in the upper half-plane but `migrates' to the lower half-plane at a positive time. Here we consider variants of Huisken's problem for open cur
Externí odkaz:
http://arxiv.org/abs/2303.12516
Publikováno v:
Special Matrices, Vol 12, Iss 1, Pp 2345-2356 (2024)
We consider the convolution equation F*X=BF* X=B, where F∈R3×3F\in {{\mathbb{R}}}^{3\times 3} and B∈Rm×nB\in {{\mathbb{R}}}^{m\times n} are given and X∈Rm×nX\in {{\mathbb{R}}}^{m\times n} is to be determined. The convolution equation can be
Externí odkaz:
https://doaj.org/article/0395be2ae6d04a78ba5386280cf675cd
Autor:
Kemmochi, Tomoya
In this paper, we will show the $L^p$-resolvent estimate for the finite element approximation of the Stokes operator for $p \in \left( \frac{2N}{N+2}, \frac{2N}{N-2} \right)$, where $N \ge 2$ is the dimension of the domain. It is expected that this e
Externí odkaz:
http://arxiv.org/abs/2208.11892