Related papers: Fast numerical derivatives based on multi-interval…

We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…

This paper addresses the problem of expressing a signal as a sum of frequency components (sinusoids) wherein each sinusoid may exhibit abrupt changes in its amplitude and/or phase. The Fourier transform of a narrow-band signal, with a…

There is growing interest in learning Fourier domain sampling strategies (particularly for magnetic resonance imaging, MRI) using optimization approaches. For non-Cartesian sampling patterns, the system models typically involve non-uniform…

We describe an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension. This work is an extension of the so-called Sparse Cardinal Sine…

This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier Transformation in time, the method utilizes a fixed…

We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the…

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…

In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…

This paper proposes a locally differentially private federated learning algorithm for strongly convex but possibly nonsmooth problems that protects the gradients of each worker against an honest but curious server. The proposed algorithm…

Physical laws governing population dynamics are generally expressed as differential equations. Research in recent decades has incorporated fractional-order (non-integer) derivatives into differential models of natural phenomena, such as…

We study the asymptotic behaviour of different statistics for time series exhibiting long memory and nonstationarity. For processes with memory parameter $d\in(-1/2,3/2)$, we derive the joint limiting distribution of discrete Fourier…

While local basis function (LBF) estimation algorithms, commonly used for identifying/tracking systems with time-varying parameters, demonstrate good performance under the assumption of normally distributed measurement noise, the estimation…

This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…

This paper proposes a differentiator for sampled signals with bounded noise and bounded second derivative. It is based on a linear program derived from the available sample information and requires no further tuning beyond the noise and…

The problem of computing the Fourier Transform of a signal whose spectrum is dominated by a small number $k$ of frequencies quickly and using a small number of samples of the signal in time domain (the Sparse FFT problem) has received…

We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions…

Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In some special cases…

Inspired by path-integral solutions to the quantum relaxation problem, we develop a numerical method to solve classical stochastic differential equations with multiplicative noise that avoids averaging over trajectories. To test the method,…

We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential…

We present and implement the concept of the Fourier-domain dedispersion (FDD) algorithm, a brute-force incoherent dedispersion algorithm. This algorithm corrects the frequency-dependent dispersion delays in the arrival time of radio…