Related papers: A Digital-Discrete Method For Smooth-Continuous Da…
We present a closed-form finite-dimensional projection method for regularizing a function defined by a discrete set of measurement data, which have been contaminated by random, zero mean errors, and for estimating the derivative and…
Presented here is a preliminary study of a strictly linear, discontinuous-Petrov-Galerkin scheme for the discrete-ordinates method in slab geometry. By ``linear'', we mean the discretization does not depend on the solution itself as is the…
The known Complex Step Derivative (CSD) method allows easy and accurate differentiation up to machine precision of real analytic functions by evaluating them a small imaginary step next to the real number line. The current paper proposes…
Detecting slender, overlapping structures remains a challenge in computational microscopy. While recent coordinate-based approaches improve detection, they often produce less accurate splines than pixel-based methods. We introduce a…
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…
In this paper we consider discrete gradient methods for approximating the solution and preserving a first integral (also called a constant of motion) of autonomous ordinary differential equations. We prove under mild conditions for a large…
We establish fully-discrete a priori and semi-discrete in time a posteriori error estimates for a discontinuous-continuous Galerkin discretization of the wave equation in second order formulation; the resulting method is a Petrov-Galerkin…
Discrete conjugate systems are quadrilateral nets with all planar faces. Discrete orthogonal systems are defined by the additional property of all faces being concircular. Their geometric properties allow one to consider them as proper…
Median regression analysis has robustness properties which make it attractive compared with regression based on the mean, while differential privacy can protect individual privacy during statistical analysis of certain datasets. In this…
This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries in the finite volume approach. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
In this paper we shall introduce a simple, effective numerical method for finding differential operators for scalar and vector-valued functions on surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute…
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
Differentially private synthetic data enables the sharing and analysis of sensitive datasets while providing rigorous privacy guarantees for individual contributors. A central challenge is to achieve strong utility guarantees for meaningful…
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
The aim of this work is to construct efficient finite volume schemes for the numerical study of sediment transport in shallow water, in the framework of the Exner model.In most cases, the velocity related to the sediment is much lower that…
We propose novel smooth approximations to the classical rounding function, suitable for differentiable optimization and machine learning applications. Our constructions are based on two approaches: (1) localized sigmoid window functions…