arXiv subjects

Maciej Goćwin

Publications and source records attributed to Maciej Goćwin.

2 recordsLinked to original sources

arXiv2020

Randomized Runge-Kutta method -- stability and convergence under inexact information

We deal with optimal approximation of solutions of ODEs under local Lipschitz condition and inexact discrete information about the right-hand side functions. We show that the randomized two-stage Runge-Kutta scheme is the optimal method among all randomized algorithms based on standard noisy information. We perform numerical experiments that confirm our theoretical findings. Moreover, for the optimal algorithm we rigorously investigate properties of regions of absolute stability.

math.NA↗

arXiv2018

On the quantum complexity of approximating median of continuous distribution

We consider approximating of the median of absolutely continuous distribution given by a probability density function $f$. We assume that $f$ has $r$ continuous derivatives, with derivative of order $r$ being Hölder continuous with the exponent $ρ$. We study the $ε$-complexity of this problem in the quantum setting. We show that the $ε$-complexity up to logarithmic factor is of order $ε^{-1/((r+ρ+1))}$.

math.NA↗