Zobrazeno 1 - 10
of 105
pro vyhledávání: '"65L06, 65L20"'
We study the connections between ordinary differential equations and optimization algorithms in a non-Euclidean setting. We propose a novel accelerated algorithm for minimising convex functions over a convex constrained set. This algorithm is a natur
Externí odkaz:
http://arxiv.org/abs/2410.19380
Nesterov's acceleration in continuous optimization can be understood in a novel way when Nesterov's accelerated gradient (NAG) method is considered as a linear multistep (LM) method for gradient flow. Although the NAG method for strongly convex funct
Externí odkaz:
http://arxiv.org/abs/2404.10238
Recently, a stability theory has been developed to study the linear stability of modified Patankar--Runge--Kutta (MPRK) schemes. This stability theory provides sufficient conditions for a fixed point of an MPRK scheme to be stable as well as for the
Externí odkaz:
http://arxiv.org/abs/2309.01562
Strong stability is a property of time integration schemes for ODEs that preserve temporal monotonicity of solutions in arbitrary (inner product) norms. It is proved that explicit Runge--Kutta schemes of order $p\in 4\mathbb{N}$ with $s=p$ stages for
Externí odkaz:
http://arxiv.org/abs/2308.05689
We revisit the general framework introduced by Fazylab et al. (SIAM J. Optim. 28, 2018) to construct Lyapunov functions for optimization algorithms in discrete and continuous time. For smooth, strongly convex objective functions, we relax the require
Externí odkaz:
http://arxiv.org/abs/2305.08658
Autor:
Reisch, Cordula, Ranocha, Hendrik
We guide the reader on a journey through mathematical modeling and numerical analysis, emphasizing the crucial interplay of both disciplines. Targeting undergraduate students with basic knowledge in dynamical systems and numerical methods for ordinar
Externí odkaz:
http://arxiv.org/abs/2304.02365
Autor:
Moisa, Andrew, Faleichik, Boris
Stabilized methods (also called Chebyshev methods) are explicit methods with extended stability domains along the negative real axis. These methods are intended for large mildly stiff problems, originating mainly from parabolic PDEs. In this paper we
Externí odkaz:
http://arxiv.org/abs/2303.16267
In this paper we investigate the stability properties of the so-called gBBKS and GeCo methods, which belong to the class of nonstandard schemes and preserve the positivity as well as all linear invariants of the underlying system of ordinary differen
Externí odkaz:
http://arxiv.org/abs/2301.10658
Autor:
Hoang, Nguyen S.
A class of explicit pseudo two-step Runge-Kutta-Nystr\"{o}m (GEPTRKN) methods for solving second-order initial value problems $y'' = f(t,y,y')$, $y(t_0) = y_0$, $y'(t_0)=y'_0$ has been studied. This new class of methods can be considered a generalize
Externí odkaz:
http://arxiv.org/abs/2207.08260
Multirate integration uses different time step sizes for different components of the solution based on the respective transient behavior. For inter/extrapolation-based multirate schemes, we construct a new subclass of schemes by using clamped cubic s
Externí odkaz:
http://arxiv.org/abs/2207.02732