Related papers: On the Discretization of Robust Exact Filtering Di…
We study the task of smoothing a circuit, i.e., ensuring that all children of a plus-gate mention the same variables. Circuits serve as the building blocks of state-of-the-art inference algorithms on discrete probabilistic graphical models…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
Many multiscale problems have a high contrast, which is expressed as a very large ratio between the media properties. The contrast is known to introduce many challenges in the design of multiscale methods and domain decomposition…
A linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrodinger-Hirota equation. Optimal, second order convergence in the discrete $H^1-$norm is proved,…
In this paper, we study the discrete time filtering problems for linear systems driven by fractional noises. The main difficulty comes from the non-Markovian of the noises. We construct the difference equation of the covariance process…
The dynamic environment in the real world calls for the adaptive techniques for information filtering, namely to provide real-time responses to the changes of system data. Where many incremental algorithms are designed for this purpose,…
This report considers linear multistep methods through time filtering. The approach has several advantages. It is modular and requires the addition of only one line of additional code. Error estimation and variable timesteps is…
Stability is an important aspect of numerical methods for hyperbolic conservation laws and has received much interest. However, continuity in time is often assumed and only semidiscrete stability is studied. Thus, it is interesting to…
Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical…
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…
The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schr\"odinger-type equations and systems with a weak nonlinearity. To make a temporal step of the compact implicit scheme we…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
Deployment of optimization algorithms over communication networks face challenges associated with time delays and corruptions. Fixed time delays can destabilize popular gradient-based algorithms, and this degradation is exacerbated by…
We propose a general strategy to discretize the Dyson series without applying direct numerical quadrature to high-dimensional integrals, and extend this framework to open quantum systems. The resulting discretization can also be interpreted…
Many numerical techniques for the description of quantum systems that are coupled to a continuous bath require the discretization of the latter. To this end, a wealth of methods has been developed in the literature, which we classify as (i)…
In this paper, a multiscale approach with partially explicit time discretization is proposed. The idea is to use a partially explicit time scheme, considering a filtration problem in a fractured medium, where the implicit scheme is used for…
The 2-step staggered (also called leap-frog) time discretisation of linear 2nd-order Hamiltonian systems (typically linear elastodynamics in a stress-velocity form) is extended for a 3-step staggered discretisation applicable for systems…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
We propose a new class of robust and Fisher-consistent estimators for mixture models. These estimators can be used to construct robust model-based clustering procedures. We study in detail the case of multivariate normal mixtures and…
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use…