Related papers: The Lanczos Tau Framework for Time-Delay Systems: …
In this article, we focus on the error that is committed when computing the matrix logarithm using the Gauss--Legendre quadrature rules. These formulas can be interpreted as Pad\'e approximants of a suitable Gauss hypergeometric function.…
We show numerically that the lowest eigenmodes of the 2-dimensional Laplace-operator with SU(2) gauge couplings are strongly localized. A connection is drawn to the Anderson-Localization problem. A new Multigrid algorithm, capable to deal…
We present a unified framework for the construction of localized exponential integrators that bypasses the traditional trade-off between the accuracy of global spectral methods and the efficiency of sparse finite differences. By evaluating…
Scalable machine learning over big data is an important problem that is receiving a lot of attention in recent years. On popular distributed environments such as Hadoop running on a cluster of commodity machines, communication costs are…
We prove a general criterion providing sufficient conditions under which a time-discretiziation of a given Stochastic Differential Equation (SDE) is a uniform in time approximation of the SDE. The criterion is also, to a certain extent,…
In this paper, we discretize the Caputo time derivative of order \alpha \in (0,1) using the Alikhanov scheme on a quasi-graded temporal mesh, and employ the Newton linearization method to approximate the nonlinear term. This yields a…
In this paper, a non-uniform time-stepping convex-splitting numerical algorithm for solving the widely used time-fractional Cahn-Hilliard equation is introduced. The proposed numerical scheme employs the $L1^+$ formula for discretizing the…
We present an improved analysis of the Euler-Maruyama discretization of the Langevin diffusion. Our analysis does not require global contractivity, and yields polynomial dependence on the time horizon. Compared to existing approaches, we…
Time-parallel methods can reduce the wall clock time required for the accurate numerical solution of differential equations by parallelizing across the time-dimension. In this paper, we present and test the convergence behavior of a…
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…
The synchronization behavior of delay coupled chaotic smooth unimodal maps over a ring network with stochastic switching of links at every time step is reported in this paper. It is observed that spatiotemporal synchronization never appears…
Gapped periodic quantum systems exhibit an interesting Localization Dichotomy, which emerges when one looks at the localization of the optimally localized Wannier functions associated to the Bloch bands below the gap. As recently proved,…
The distribution of the eigenvalues of a Hermitian matrix (or of a Hermitian matrix pencil) reveals important features of the underlying problem, whether a Hamiltonian system in physics, or a social network in behavioral sciences. However,…
We propose two kinds of model order reduction methods for discrete time-delay systems with inhomogeneous initial conditions. The peculiar properties of discrete Walsh functions are directly utilized to compute the Walsh coefficients of the…
Reducing communication complexity is critical for efficient decentralized optimization. The proximal decentralized optimization (PDO) framework is particularly appealing, as methods within this framework can exploit functional similarity…
The next-to-next-to-leading order perturbative QCD corrections to R_tau and the higher moments of the invariant mass distribution in the hadronic tau decays are considered. The renormalization scheme dependence of these corrections is…
Orthogonal time frequency space (OTFS) modulation is a robust candidate waveform for future wireless systems, particularly in high-mobility scenarios, as it effectively mitigates the impact of rapidly time-varying channels by mapping…
We target time-dependent partial differential equations (PDEs) with heterogeneous coefficients in space and time. To tackle these problems, we construct reduced basis/ multiscale ansatz functions defined in space that can be combined with…
In this paper, we propose and analyze an explicit time-stepping scheme for a spatial discretization of stochastic Cahn--Hilliard equation with additive noise. The fully discrete approximation combines a spectral Galerkin method in space…
This paper presents a new algorithm for set-based state estimation of nonlinear discrete-time systems with bounded uncertainties. The novel method builds upon essential properties and computational advantages of constrained zonotopes (CZs)…