4 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…