Related papers: Obtaining Pseudo-inverse Solutions With MINRES
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…
Despite the rich existing literature about minimax optimization in continuous settings, only very partial results of this kind have been obtained for combinatorial settings. In this paper, we fill this gap by providing a characterization of…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
We consider the problem of inferring the total causal effect of a single variable intervention on a (response) variable of interest. We propose a certain marginal integration regression technique for a very general class of potentially…
A new variant of the GMRES method is presented for solving linear systems with the same matrix and subsequently obtained multiple right-hand sides. The new method keeps such properties of the classical GMRES algorithm as follows. Both bases…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
In this work, we fully explore three refined convergence structures of the lowest-order rectangular Raviart-Thomas element in solving the Laplace eigenvalue problem. Firstly, the scheme possesses a property of supercloseness between the…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
The uniqueness of sparsest solutions of underdetermined linear systems plays a fundamental role in the newly developed compressed sensing theory. Several new algebraic concepts, including the sub-mutual coherence, scaled mutual coherence,…
The fundamental problem of our interest here is soft-input soft-output multiple-input multiple-output (MIMO) detection. We propose a method, referred to as subspace marginalization with interference suppression (SUMIS), that yields…
We present a fourth-order projection method with adaptive mesh refinement (AMR) for numerically solving the incompressible Navier-Stokes equations (INSE) with subcycling in time. Our method features (i) a reformulation of INSE so that the…
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…
Mixed Binary Quadratic Programs (MBQPs) are a class of NP-hard problems that arise in a wide range of applications, including finance, machine learning, and chemical and energy systems. Large-scale MBQPs are challenging to solve with exact…
Spectral element methods (SEM), which are extensions of finite element methods (FEM), are important emerging techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver better accuracy due…
Motivated by a recent work on a preconditioned MINRES for flipped linear systems in imaging, in this note we extend the scope of that research for including more precise boundary conditions such as reflective and anti-reflective ones. We…
By setting up appropriate uniform convergence structures, we are able to reformulate the Order Completion Method of Oberguggenberger and Rosinger in a setting that more closely resembles the usual topological constructions for solving PDEs.…
Our study is motivated by the solution of Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique, an iterative method whose main characteristic is that of solving,…
We analyze and test using Fourier extensions that minimize a Hilbert space norm for the purpose of solving partial differential equations (PDEs) on surfaces. In particular, we prove that the approach is arbitrarily high-order and also show…
This paper develops the preconditioning technique as a method to address the accuracy issue caused by ill-conditioning. Given a preconditioner $M$ for an ill-conditioned linear system $Ax=b$, we show that, if the inverse of the…