相关论文: A Weighted Least-Squares Transport Equation Compat…

The diffusion least mean square (DLMS) and the diffusion normalized least mean square (DNLMS) algorithms are analyzed for a network having a fusion center. This structure reduces the dimensionality of the resulting stochastic models while…

We investigate the accuracy of the recently proposed nonclassical transport equation. This equation contains an extra independent variable compared to the classical transport equation (the path-length $s$), and models particle transport…

We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus…

In this article, we present a method for increasing adaptivity of an existing robust estimation algorithm by learning two parameters to better fit the residual distribution. The analyzed method uses these two parameters to calculate weights…

We consider the least-squares finite element method (lsfem) for systems of nonlinear ordinary differential equations and establish an optimal error estimate for this method when piecewise linear elements are used. The main assumptions are…

Optimal transport has recently started to be successfully employed to define misfit or loss functions in inverse problems. However, it is a problem intrinsically defined for positive (probability) measures and therefore strategies are…

An improvement modification of the Spectral Approach (SA) used for approximating the nonclassical neutral particle transport equation is described in this work. The main focus of the modified SA lies on a slight modification of the…

We consider the problem of self-localization by a resource-constrained mobile node given perturbed anchor position information and distance estimates from the anchor nodes. We consider normally-distributed noise in anchor position…

Least squares (LS) fitting is one of the most fundamental techniques in science and engineering. It is used to estimate parameters from multiple noisy observations. In many problems the parameters are known a-priori to be bounded integer…

We define and analyse a least-squares finite element method for a first-order reformulation of the obstacle problem. Moreover, we derive variational inequalities that are based on similar but non-symmetric bilinear forms. A priori error…

Two reconstruction methods of Electrical Impedance Tomography (EIT) are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optics (CGO) solutions to D-bar equations involving the global…

We study data-driven least squares (LS) problems with semidefinite (SD) constraints and derive finite-sample guarantees on the spectrum of their optimal solutions when these constraints are relaxed. In particular, we provide a high…

Based on a microcanonical picture that maps the steady-state quantum transport process to a drain-to-source excitation, we develop a constrained-search density functional formalism for finite-bias quantum transport calculations. By…

Nowadays, Non-Linear Least-Squares embodies the foundation of many Robotics and Computer Vision systems. The research community deeply investigated this topic in the last years, and this resulted in the development of several open-source…

Recently, a Levenberg-Marquardt method with Singular Scaling matrix, called LMMSS, was proposed and successfully applied in parameter estimation in heat conduction problems, where the choice of suitable singular scaling matrix resulted in…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

We propose a Binary Robust Least Squares (BRLS) model that encompasses key robust least squares formulations, such as those involving uncertain binary labels and adversarial noise constrained within a hypercube. We show that the geometric…

In this work, we develop a distributed least squares approximation (DLSA) method that is able to solve a large family of regression problems (e.g., linear regression, logistic regression, and Cox's model) on a distributed system. By…

We propose an efficient algorithm for solving group synchronization under high levels of corruption and noise, while we focus on rotation synchronization. We first describe our recent theoretically guaranteed message passing algorithm that…

We present preconditioned stochastic gradient descent (SGD) algorithms for the $\ell_1$ minimization problem $\min_{x}\|A x - b\|_1$ in the overdetermined case, where there are far more constraints than variables. Specifically, we have $A…