Related papers: A row space method for solving a system of linear …
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
In this paper, we consider the iterative solution of linear algebraic equations under the condition that matrix-vector products with the coefficient matrix are computed only partially. At the same time, non-computed entries are set to…
The Kaczmarz algorithm is an iterative method that solves linear systems of equations. It stands out among iterative algorithms when dealing with large systems for two reasons. First, at each iteration, the Kaczmarz algorithm uses a single…
Based on the geometric {\it Triangle Algorithm} for testing membership of a point in a convex set, we present a novel iterative algorithm for testing the solvability of a real linear system $Ax=b$, where $A$ is an $m \times n$ matrix of…
New solution method for the systems of linear equations in commutative integral domains is proposed. Its complexity is the same that the complexity of the matrix multiplication.
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
In applications, a substantial number of problems can be formulated as non-linear least squares problems over smooth varieties. Unlike the usual least squares problem over a Euclidean space, the non-linear least squares problem over a…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
Inverse problems are inherently ill-posed and therefore require regularization techniques to achieve a stable solution. While traditional variational methods have well-established theoretical foundations, recent advances in machine learning…
We propose a method called ideal regression for approximating an arbitrary system of polynomial equations by a system of a particular type. Using techniques from approximate computational algebraic geometry, we show how we can solve ideal…
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
In this paper, several row and column orthogonal projection methods are proposed for solving matrix equation $AXB=C$, where the matrix $A$ and $B$ are full rank or rank deficient and equation is consistent or not. These methods are…
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…
A type of iterative orthogonally accumulated projection methods for solving linear system of equations are proposed in this paper. This type of methods are applications of accumulated projection(AP) technique proposed recently by authors.…
We show that if the probabilistic logarithmic-space solver or the deterministic nearly logarithmic-space solver for undirected Laplacian matrices can be extended to solve slightly larger subclasses of linear systems, then they can be use to…
In this paper we propose a new reduced order model (ROM) to the imcompressible Stokes equations. Numerical experiments show that our ROM is accurate and efficient. Under some assumptions on the problem data, we prove that the convergence…
For approximately solving linear ill-posed problems in Hilbert spaces, we investigate the regularization properties of the aggregation method and the RatCG method. These recent algorithms use previously calculated solutions of Tikhonov…