Related papers: Solution Methods and Perturbation Analysis for the…
In our work, we consider the linear least squares problem for $m\times n$-systems of linear equations $Ax = b$, $m\geq n$, such that the matrix $A$ and right-hand side vector $b$ can vary within an interval $m\times n$-matrix and an…
It is well-known that the noise associated with the collection of an astronomical image by a CCD camera is, in large part, Poissonian. One would expect, therefore, that computational approaches that incorporate this a priori information…
The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple…
In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation $Ax=b$, where $A$ is an $m\times n$ full-rank matrix, $b$ is a column-vector of dimension $m$, and $m$ (the number of…
We propose the first general and practical framework to design certifiable algorithms for robust geometric perception in the presence of a large amount of outliers. We investigate the use of a truncated least squares (TLS) cost function,…
In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares (S-NNLS) problem. We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R-…
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…
We develop a recursive total least-squares (RTLS) algorithm for errors-in-variables system identification utilizing the inverse power method and the dichotomous coordinate-descent (DCD) iterations. The proposed algorithm, called DCD-RTLS,…
Linear regression with shuffled labels and with a noisy latent design matrix arises in many correspondence recovery problems. We propose a total least-squares approach to the problem of estimating the underlying true permutation and provide…
This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…
This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…
We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…
Given a linear regression setting, Iterative Least Trimmed Squares (ILTS) involves alternating between (a) selecting the subset of samples with lowest current loss, and (b) re-fitting the linear model only on that subset. Both steps are…
In this paper, we propose a unified non-conforming least-squares spectral element approach for solving Stokes equations with various non-standard boundary conditions. Existing least-squares formulations mostly deal with Dirichlet boundary…
We construct least squares formulations of PDEs with inhomogeneous essential boundary conditions, where boundary residuals are not measured in unpractical fractional Sobolev norms, but which formulations nevertheless are shown to yield a…
We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably…
Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulation thereof. In an implicitly constrained approach, the…
I present here a pedagogical introduction to the works by Rashel Tublin and Yan V. Fyodorov on random linear systems with quadratic constraints, using tools from Random Matrix Theory and replicas. These notes illustrate and complement the…