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We propose a fast method to approximate the real stability radius of a linear dynamical system with output feedback, where the perturbations are restricted to be real valued and bounded with respect to the Frobenius norm. Our work builds on…
A parametric constrained convex optimal control problem, where the initial state is perturbed and the linear state equation contains a noise, is considered in this paper. Formulas for computing the subdifferential and the singular…
Spectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential…
We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
We apply a recently proposed method for the analysis of time series from systems with delayed feedback to experimental data generated by a CO_2 laser. The method is able to estimate the delay time with an error of the order of the sampling…
Based on neural network and adaptive subspace approximation method, we propose a new machine learning method for solving partial differential equations. The neural network is adopted to build the basis of the finite dimensional subspace.…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
The Sparse Identification of Nonlinear Dynamics (SINDy) framework has been frequently used to discover parsimonious differential equations governing natural and physical systems. This includes recent extensions to SINDy that enable the…
This work establishes the first rigorous stability guarantees for approximate predictors in delay-adaptive control of nonlinear systems, addressing a key challenge in practical implementations where exact predictors are unavailable. We…
Discrete-time stochastic systems are an essential modelling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification…
In this work we introduce the notion of an angular spectrum for a linear discrete time nonautonomous dynamical system. The angular spectrum comprises all accumulation points of longtime averages formed by maximal principal angles between…
Pseudospectral schemes are a class of numerical methods capable of solving smooth problems with high accuracy thanks to their exponential convergence to the true solution. When applied to discontinuous problems, such as fluid shocks and…
We consider parameterized variational inverse problems that are constrained by partial differential equations (PDEs). We seek to efficiently compute the solution of the inverse problem when auxiliary model parameters, which appear in the…
In the design of integrated circuits, one critical metric is the maximum delay introduced by combinational modules within the circuit. This delay is crucial because it represents the time required to perform a computation: in an…
Standard high-dimensional regression methods assume that the underlying coefficient vector is sparse. This might not be true in some cases, in particular in presence of hidden, confounding variables. Such hidden confounding can be…
A linear Gaussian state-space smoothing algorithm is presented for estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements…
In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…
In this paper, we consider a class of difference-of-convex (DC) optimization problems, which require only a weaker restricted $L$-smooth adaptable property on the smooth part of the objective function, instead of the standard global…
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…