Related papers: On the Discretization of Robust Exact Filtering Di…
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This…
Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, applying this paradigm to Transformer is…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
This paper studies the two-stage fourth-order accurate time discretization \cite{LI-DU:2016} and applies it to special relativistic hydrodynamical equations. It is shown that new two-stage fourth-order accurate time discretizations can be…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
A novel switching differentiator that has considerably simple form is proposed. Under the assumption that time-derivatives of the signal are norm-bounded, it is shown that estimation errors are convergent to the zeros asymptotically. The…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
While differentially private synthetic data generation has been explored extensively in the literature, how to update this data in the future if the underlying private data changes is much less understood. We propose an algorithmic…
Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…
This paper presents a formal framework and proposes algorithms to extend forecast reconciliation to discrete-valued data to extend forecast reconciliation to discrete-valued data, including low counts. A novel method is introduced based on…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…
This paper is devoted to filtering, smoothing, and prediction of polynomial processes that are partially observed. These problems are known to allow for an explicit solution in the simpler case of linear Gaussian state space models. The key…
We present the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. Given a system of differential equations possessing conservation laws, our approach is based on…
An algorithm for the estimation of multiple targets from partial and corrupted observations is introduced based on the concept of partially-distinguishable multi-target system. It combines the advantages of engineering solutions like MHT…
This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…
We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic wave systems that are separated by straight interfaces. Such coupled simulations allow the application of the elastic…
We consider the discrete-time filtering problem in scenarios where the observation noise is low or degenerate. We focus on the case where the observation equation is a linear function of the state and the data involve additive noise.…
Future architectures designed to deliver exascale performance motivate the need for novel algorithmic changes in order to fully exploit their capabilities. In this paper, the performance of several numerical algorithms, characterised by…
By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…