65 citations · 140 across the 28 of their papers we have counts for
29 papers
A polynomial moment approach to a rank condition for continuous-stage Runge--Kutta methods
Yuto Miyatake
In the study of energy-preserving methods for Hamiltonian systems, polynomial continuous-stage Runge--Kutta methods play an important role. Necessary and sufficient conditions for…
Modelling the discretization error of initial value problems using the Wishart distribution
Naoki Marumo, Takeru Matsuda, Yuto Miyatake
This paper presents a new discretization error quantification method for the numerical integration of ordinary differential equations. The error is modelled by using the Wishart di…
A new family of fourth-order energy-preserving integrators
Yuto Miyatake
For Hamiltonian systems with non-canonical structure matrices, a new family of fourth-order energy-preserving integrators is presented. The integrators take a form of a combination…
Structure-preserving numerical methods for constrained gradient flows of planar closed curves with explicit tangential velocities
Tomoya Kemmochi, Yuto Miyatake, Koya Sakakibara
In this paper, we consider numerical approximation of constrained gradient flows of planar closed curves, including the Willmore and the Helfrich flows. These equations have energy…
High-order linearly implicit schemes conserving quadratic invariants
Shun Sato, Yuto Miyatake, John C. Butcher
In this paper, we propose linearly implicit and arbitrary high-order conservative numerical schemes for ordinary differential equations with a quadratic invariant. Many differentia…
Composing a surrogate observation operator for sequential data assimilation
Kosuke Akita, Yuto Miyatake, Daisuke Furihata
In data assimilation, state estimation is not straightforward when the observation operator is unknown. This study proposes a method for composing a surrogate operator when the tru…
Adaptive projected SOR algorithms for nonnegative quadratic programming
Yuto Miyatake, Tomohiro Sogabe
The choice of relaxation parameter in the projected successive overrelaxation (PSOR) method for nonnegative quadratic programming problems is problem-dependent. We present novel ad…
Piecewise monotone estimation in one-parameter exponential family
Takeru Matsuda, Yuto Miyatake
The problem of estimating a piecewise monotone sequence of normal means is called the nearly isotonic regression. For this problem, an efficient algorithm has been devised by modif…
Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memory
Takashi Matsubara, Yuto Miyatake, Takaharu Yaguchi
A neural network model of a differential equation, namely neural ODE, has enabled the learning of continuous-time dynamical systems and probabilistic distributions with high accura…
Computing the matrix fractional power with the double exponential formula
Fuminori Tatsuoka, Tomohiro Sogabe, Yuto Miyatake +2
Two quadrature-based algorithms for computing the matrix fractional power are presented in this paper. These algorithms are based on the double exponential (DE) formula, whic…
Generalization of partitioned Runge--Kutta methods for adjoint systems
Takeru Matsuda, Yuto Miyatake
This study computes the gradient of a function of numerical solutions of ordinary differential equations (ODEs) with respect to the initial condition. The adjoint method computes t…
A Parallelizable Energy-Preserving Integrator MB4 and Its Application to Quantum-Mechanical Wavepacket Dynamics
Tsubasa Sakai, Shuhei Kudo, Hiroto Imachi +3
In simulating physical systems, conservation of the total energy is often essential, especially when energy conversion between different forms of energy occurs frequently. Recently…
A fully discrete curve-shortening polygonal evolution law for moving boundary problems
Koya Sakakibara, Yuto Miyatake
We consider the numerical integration of moving boundary problems with the curve-shortening property, such as the mean curvature flow and Hele-Shaw flow. We propose a fully discret…
Modified Strang splitting for semilinear parabolic problems
Kosuke Nakano, Tomoya Kemmochi, Yuto Miyatake +2
We consider applying the Strang splitting to semilinear parabolic problems. The key ingredients of the Strang splitting are the decomposition of the equation into several parts and…
Adjoint-based exact Hessian computation
Shin-ichi Ito, Takeru Matsuda, Yuto Miyatake
We consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need to extract t…
Estimation of ordinary differential equation models with discretization error quantification
Takeru Matsuda, Yuto Miyatake
We consider parameter estimation of ordinary differential equation (ODE) models from noisy observations. For this problem, one conventional approach is to fit numerical solutions (…
Relation between the T-congruence Sylvester equation and the generalized Sylvester equation
Yuki Satake, Masaya Oozawa, Tomohiro Sogabe +3
The T-congruence Sylvester equation is the matrix equation , where , , and $C\in\mathbb{R}^{m\times m}…
A structure-preserving Fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schrödinger equation
Yuto Miyatake, Tai Nakagawa, Tomohiro Sogabe +1
We propose a Fourier pseudo-spectral scheme for the space-fractional nonlinear Schrödinger equation. The proposed scheme has the following features: it is linearly implicit, it pre…
Algorithms for the computation of the matrix logarithm based on the double exponential formula
Fuminori Tatsuoka, Tomohiro Sogabe, Yuto Miyatake +1
We consider the computation of the matrix logarithm by using numerical quadrature. The efficiency of numerical quadrature depends on the integrand and the choice of quadrature form…
Structure-preserving model reduction for dynamical systems with a first integral
Yuto Miyatake
Since the expense of the numerical integration of large scale dynamical systems is often computationally prohibitive, model reduction methods, which approximate such systems by sim…
Adaptive SOR methods based on the Wolfe conditions
Yuto Miyatake, Tomohiro Sogabe, Shao-Liang Zhang
Because the expense of estimating the optimal value of the relaxation parameter in the successive over-relaxation (SOR) method is usually prohibitive, the parameter is often adapti…
On the equivalence between SOR-type methods for linear systems and discrete gradient methods for gradient systems
Yuto Miyatake, Tomohiro Sogabe, Shao-Liang Zhang
The iterative nature of many discretisation methods for continuous dynamical systems has led to the study of the connections between iterative numerical methods in numerical linear…
Solution of the -th eigenvalue problem in large-scale electronic structure calculations
Dongjin Lee, Takeo Hoshi, Tomohiro Sogabe +2
We consider computing the -th eigenvalue and its corresponding eigenvector of a generalized Hermitian eigenvalue problem of large sparse matrices. In electronic stru…
A cost-efficient variant of the incremental Newton iteration for the matrix th root
Fuminori Tatsuoka, Tomohiro Sogabe, Yuto Miyatake +1
Incremental Newton (IN) iteration, proposed by Iannazzo, is stable for computing the matrix th root, and its computational cost is flops per iteration. In th…