Related papers: Randomized Kaczmarz with Averaging
Recently, the randomized sparse Kaczmarz method has been accelerated by designing heavy ball momentum adaptively via a minimal-error principle. In this paper, we develop a new adaptive momentum method based on the minimal dual function…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…
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 propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation…
We consider linear systems $Ax = b$ where $A \in \mathbb{R}^{m \times n}$ consists of normalized rows, $\|a_i\|_{\ell^2} = 1$, and where up to $\beta m$ entries of $b$ have been corrupted (possibly by arbitrarily large numbers). Haddock,…
Matrix factorization techniques compute low-rank product approximations of high dimensional data matrices and as a result, are often employed in recommender systems and collaborative filtering applications. However, many algorithms for this…
An iterative method LSMR is presented for solving linear systems $Ax=b$ and least-squares problem $\min \norm{Ax-b}_2$, with $A$ being sparse or a fast linear operator. LSMR is based on the Golub-Kahan bidiagonalization process. It is…
Stochastic iterative algorithms such as the Kaczmarz and Gauss-Seidel methods have gained recent attention because of their speed, simplicity, and the ability to approximately solve large-scale linear systems of equations without needing to…
A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…
Adaptive cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems involving a shifted Hessian in the spirit of the Levenberg-Marquardt and trust-region methods. The standard approach consists in…
Existing block Kaczmarz methods face challenges in balancing computational efficiency and convergence for large sparse linear systems with scattered nonzero patterns, due to costly partitioning strategies and non-orthogonal projections. In…
Recovering a signal $x^\ast \in \mathbb{R}^n$ from a sequence of linear measurements is an important problem in areas such as computerized tomography and compressed sensing. In this work, we consider an online setting in which measurements…
The Kaczmarz algorithm is an iterative method for solving a system of linear equations. It can be extended so as to reconstruct a vector $x$ in a (separable) Hilbert space from the inner-products $\{\langle x, \phi_{n} \rangle\}$. The…
The randomized coordinate descent (RCD) method is a classical algorithm with simple, lightweight iterations that is widely used for various optimization problems, including the solution of positive semidefinite linear systems. As a linear…
The generalized Gearhart-Koshy acceleration is a recent exact affine search technique designed for the method of cyclic projections onto hyperplanes, i.e., the Kaczmarz method. However, its convergence properties, particularly the linear…
Distributed linear algebraic equation over networks, where nodes hold a part of problem data and cooperatively solve the equation via node-to-node communications, is a basic distributed computation task receiving an increasing research…
The reconstruction of tensor-valued signals from corrupted measurements, known as tensor regression, has become essential in many multi-modal applications such as hyperspectral image reconstruction and medical imaging. In this work, we…
The Douglas-Rachford (DR) method is a widely used method for finding a point in the intersection of two closed convex sets (feasibility problem). However, the method converges weakly and the associated rate of convergence is hard to analyze…
For solving a consistent system of linear equations, the classical row-action (also known as Kaczmarz) method is a simple while really effective iteration solver. Based on the greedy index selection strategy and Polyak's heavy-ball momentum…
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without addi- tional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the…