11 citations · 55 across the 23 of their papers we have counts for
24 papers
Convergence analysis of dynamical systems for optimization by an improved Lyapunov framework
Atsushi Tabei, Ken'ichiro Tanaka
We study the convergence analysis of continuous-time dynamical systems associated with optimization methods for strongly convex functions. Recent works have proposed systematic con…
Computer-Assisted Search for Differential Equations Corresponding to Optimization Methods and Their Convergence Rates
Atsushi Tabei, Ken'ichiro Tanaka
Let be a continuously differentiable convex function with its minimizer denoted by and optimal value . Optimization algorithms s…
Computation of the exponential function of matrices by a formula without oscillatory integrals on infinite intervals
Masato Suzuki, Ken'ichiro Tanaka
We propose a quadrature-based formula for computing the exponential function of matrices with a non-oscillatory integral on an infinite interval and an oscillatory integral on a fi…
How sharp are error bounds? --lower bounds on quadrature worst-case errors for analytic functions
Takashi Goda, Yoshihito Kazashi, Ken'ichiro Tanaka
Numerical integration over the real line for analytic functions is studied. Our main focus is on the sharpness of the error bounds. We first derive two general lower estimates for…
Accelerated gradient descent method for functionals of probability measures by new convexity and smoothness based on transport maps
Ken'ichiro Tanaka
We consider problems of minimizing functionals of probability measures on the Euclidean space. To propose an accelerated gradient descent algorithm for such problems,…
Wavelet characterization of exponentially weighted Besov space with dominating mixed smoothness and its application to function approximation
Yoshihiro Kogure, Ken'ichiro Tanaka
Although numerous studies have focused on normal Besov spaces, limited studies have been conducted on exponentially weighted Besov spaces. Therefore, we define exponentially weight…
Skeleton structure inherent in discrete-time quantum walks
Tomoki Yamagami, Etsuo Segawa, Ken'ichiro Tanaka +4
In this paper, we claim that a common underlying structure--a skeleton structure--is present behind discrete-time quantum walks (QWs) on a one-dimensional lattice with a homogeneou…
Convergence rates for energies of interacting particles whose distribution spreads out as their number increases
Patrick van Meurs, Ken'ichiro Tanaka
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of…
Yet another DE-Sinc indefinite integration formula
Tomoaki Okayama, Ken'ichiro Tanaka
Based on the Sinc approximation combined with the tanh transformation, Haber derived an approximation formula for numerical indefinite integration over the finite interval (-1, 1).…
Sparser Kernel Herding with Pairwise Conditional Gradients without Swap Steps
Kazuma Tsuji, Ken'ichiro Tanaka, Sebastian Pokutta
The Pairwise Conditional Gradients (PCG) algorithm is a powerful extension of the Frank-Wolfe algorithm leading to particularly sparse solutions, which makes PCG very appealing for…
Sparse solutions of the kernel herding algorithm by improved gradient approximation
Kazuma Tsuji, Ken'ichiro Tanaka
The kernel herding algorithm is used to construct quadrature rules in a reproducing kernel Hilbert space (RKHS). While the computational efficiency of the algorithm and stability o…
Kernel quadrature by applying a point-wise gradient descent method to discrete energies
Ken'ichiro Tanaka
We propose a method for generating nodes for kernel quadrature by a point-wise gradient descent method. For kernel quadrature, most methods for generating nodes are based on the wo…
Monte Carlo construction of cubature on Wiener space
Satoshi Hayakawa, Ken'ichiro Tanaka
In this paper, we investigate application of mathematical optimization to construction of a cubature formula on Wiener space, which is a weak approximation method of stochastic dif…
Maximum likelihood estimation of the Fisher-Bingham distribution via efficient calculation of its normalizing constant
Yici Chen, Kenichiro Tanaka
This paper proposes an efficient numerical integration formula to compute the normalizing constant of Fisher--Bingham distributions. This formula uses a numerical integration formu…
Convergence analysis of approximation formulas for analytic functions via duality for potential energy minimization
Satoshi Hayakawa, Ken'ichiro Tanaka
We investigate the approximation formulas that were proposed by Tanaka & Sugihara (2019), in weighted Hardy spaces, which are analytic function spaces with certain asymptotic decay…
Construction of conformal maps based on the locations of singularities for improving the double exponential formula
Shunki Kyoya, Ken'ichiro Tanaka
The double exponential formula, or the DE formula, is a high-precision integration formula using a change of variables called a DE transformation; whereas there is a disadvantage t…
Generation of point sets by convex optimization for interpolation in reproducing kernel Hilbert spaces
Ken'ichiro Tanaka
We propose algorithms to take point sets for kernel-based interpolation of functions in reproducing kernel Hilbert spaces (RKHSs) by convex optimization. We consider the case of ke…
Counting Integral Points in Polytopes via Numerical Analysis of Contour Integration
Hiroshi Hirai, Ryunosuke Oshiro, Ken'ichiro Tanaka
In this paper, we address the problem of counting integer points in a rational polytope described by , where is an $n \t…
Design of accurate formulas for approximating functions in weighted Hardy spaces by discrete energy minimization
Ken'ichiro Tanaka, Masaaki Sugihara
We propose a simple and effective method for designing approximation formulas for weighted analytic functions. We consider spaces of such functions according to weight functions ex…
An optimal approximation formula for functions with singularities
Ken'ichiro Tanaka, Tomoaki Okayama, Masaaki Sugihara
We propose an optimal approximation formula for analytic functions that are defined on a complex region containing the real interval and possibly have algebraic singularit…
Potential theoretic approach to design of accurate formulas for function approximation in symmetric weighted Hardy spaces
Ken'ichiro Tanaka, Tomoaki Okayama, Masaaki Sugihara
We propose a method for designing accurate interpolation formulas on the real axis for the purpose of function approximation in weighted Hardy spaces. In particular, we consider th…
Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis
Ken'ichiro Tanaka, Alexis Akira Toda
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which ari…
Error control of a numerical formula for the Fourier transform by Ooura's continuous Euler transform and fractional FFT
Ken'ichiro Tanaka
In this paper, we consider a method for fast numerical computation of the Fourier transform of a slowly decaying function with given accuracy in given ranges of the frequency. In t…
Convergence Rates and Explicit Error Bounds of Hill's Method for Spectra of Self-Adjoint Differential Operators
Ken'ichiro Tanaka, Sunao Murashige
We present the convergence rates and the explicit error bounds of Hill's method, which is a numerical method for computing the spectra of ordinary differential operators with perio…