Related papers: PLSS: A Projected Linear Systems Solver
We propose a new deterministic Kaczmarz algorithm for solving consistent linear systems $A\mathbf{x}=\mathbf{b}$. Basically, the algorithm replaces orthogonal projections with reflections in the original scheme of Stefan Kaczmarz. Building…
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…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…
Scaling hyperparameter optimisation to very large datasets remains an open problem in the Gaussian process community. This paper focuses on iterative methods, which use linear system solvers, like conjugate gradients, alternating…
Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large…
The main computational cost of algorithms for computing reduced-order models of parametric dynamical systems is in solving sequences of very large and sparse linear systems. We focus on efficiently solving these linear systems, arising…
We develop two greedy sampling rules for the Sketch & Project method for solving linear feasibility problems. The proposed greedy sampling rules generalize the existing max-distance sampling rule and uniform sampling rule and generate…
Stochastic computing (SC) is a promising candidate for fault tolerant computing in digital circuits. We present a novel stochastic computing estimation architecture allowing to solve a large group of estimation problems including least…
The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for the iterates and analyze their convergence behaviour both…
Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive. Iterative solvers, on the other hand, demonstrate better scalability; but, need to be used with an appropriate preconditioner (e.g.,…
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…
Linear constrained switching systems are linear switched systems whose switching sequences are constrained by a deterministic finite automaton. This work investigates how to generate a sequence of matrices with an asymptotic growth rate…
In this paper we propose an identification method for latent-variable graphical models associated to autoregressive (AR) Gaussian stationary processes. The identification procedure exploits the approximation of AR processes through…
We propose a novel Linear Program (LP) based formula- tion for solving jigsaw puzzles. We formulate jigsaw solving as a set of successive global convex relaxations of the stan- dard NP-hard formulation, that can describe both jigsaws with…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…
This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x}_* \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x}_* = \mathbf{b}$. In the approach a standard iterative…