Related papers: Correction to: "Blind maximum likelihood separatio…
In high-contrast composite materials, the electric field concentration is a common phenomenon when two inclusions are close to touch. It is important from an engineering point of view to study the dependence of the electric field on the…
The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…
Particle acceleration in plasma creates a possibility of exceptionally high accelerating gradients and appears as a very attractive option for future linear electron-positron and/or photon-photon colliders. These high accelerating gradients…
We give an improved lower bound for the $L_2$-discrepancy of finite point sets in the unit square.
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
The framework of Integral Quadratic Constraints (IQCs) is used to perform an analysis of gradient descent with varying step sizes. Two performance metrics are considered: convergence rate and noise amplification. We assume that the step…
The present paper continues our investigation of an implementation of a least-squares collocation method for higher-index differential-algebraic equations. In earlier papers, we were able to substantiate the choice of basis functions and…
We explain an error in our paper "A smooth foliation of the 5-sphere by complex surfaces", Ann. Math 156 (2002), p.915-930.
The original versions (1 and 2) of this paper paper contain a fatal error. All my attempts to patch the error have failed. As a service to the community I explain the error in some detail.
New error bounds for the linear complementarity problems are given respectively when the involved matrices are Nekrasov matrices and B-Nekrasov matrices. Numerical examples are given to show that new bounds are better respectively than…
We point out an issue with Lemma 8.6 of [1]. This lemma specifies the required sample complexity for recovering the delay-Doppler pairs in radar systems. In this lemma, it is claimed that the required sample complexity is linearly related…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…
When training neural networks with low-precision computation, rounding errors often cause stagnation or are detrimental to the convergence of the optimizers; in this paper we study the influence of rounding errors on the convergence of the…
In this paper the maximum likelihood equations for the parameters of the Weight Lindley distribution are studied considering different types of censoring, such as, type I, type II and random censoring mechanism. A numerical simulation study…
We study the convergence of the Augmented Decomposition Algorithm (ADA) proposed in [32] for solving multi-block separable convex minimization problems subject to linear constraints. We show that the global convergence rate of the exact ADA…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…
In these proceedings a novel approach to deal with the beam-induced effects in luminosity measurement is presented. Based on the relativistic kinematics of the collision frame of the Bhabha process, the beam-beam related uncertainties can…