Related papers: Geometrical inverse matrix approximation for least…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
In this paper we present computational experiments with the Markov Chain Monte Carlo Matrix Inversion ($(\text{MC})^2\text{MI}$) on several accelerator architectures and investigate their impact on performance and scalability of the method.…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
A matrix algorithm runs superfast (aka at sublinear cost) if it involves much fewer flops and memory cells than an input matrix has entries. Big Data are frequently represented by matrices of immense sizes that cannot be handled directly…
In this paper, a Gauss-Seidel method with oblique direction (GSO) is proposed for finding the least-squares solution to a system of linear equations, where the coefficient matrix may be full rank or rank deficient and the system is…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
In this paper, we present a progressive and iterative approximation method with memory for least square fitting(MLSPIA). It adjusts the control points and the weighted sums iteratively to construct a series of fitting curves (surfaces) with…
The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure observed in many such Inverse Problems presents severe…
In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next…
We develop a matrix approach to the Maximal Acyclic Subgraph (MAS) problem by reducing it to finding the closest nilpotent matrix to the matrix of the graph. Using recent results on the closest Schur stable systems and on minimising the…
For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…
We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual $\ell_1$ and the group lasso penalty, by allowing the subsets to overlap. Such regularizations lead to…
This work introduces, analyzes and demonstrates an efficient and theoretically sound filtering strategy to ensure the condition of the least-squares problem solved at each iteration of Anderson acceleration. The filtering strategy consists…
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…
With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of least squares (LS) problems $\min_x\|b-Ax\|_2$, where $A…
In this short article, some properties of matrices of moving least-squares approximation have been proven.The used technique is based on singular-value decomposition and inequalities for singular-values. Some inequalities for the norm of…
In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…
The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…